This is a two-part answer for different audiences. The question title may attract people interested in a solution for epoxy casting or other projects involving a substantive amount of resin. The body of the question describes needing to make a drilled hole a little smaller, so a tiny amount of resin. Two very different use cases and considerations.
1. Resin to make a hole smaller
Considerations: You need a small amount of resin. There won't be much resin surface exposed, but you don't want it transparent. Since you aren't concerned about the color, you probably don't care if the color changes over time. For a small surface area covering something that isn't backlit, it won't make much difference whether it is opaque or densely translucent.
The recommendations in these answers are likely to be better than some random powders, but you could really use a broad range of household powders that are very fine. I would still test it first, though. The materials suggested in the second part of this answer (see below), are intended to also be suitable for casting purposes. The broader range of materials in the other answers will provide additional options that will be adequate for the requirements in this question.
For this use case, the question more important than "what" is probably "how much". You can mix a small amount of opaque powder and turn the resin opaque but still liquid. This would allow you to pour it into the cavity, where it will spread out and self-level. Or use the hole as a mold by sealing one face, pour a layer of resin, and drill a new hole through it after it hardens.
Alternatively, mix in a lot of powder so that a small amount of resin serves as a binder. The mix will have a putty or clay consistency. You can push it where you want it and sculpt a solution. After it hardens, you can further smooth and shape it with tools. You could also use it the same way as liquid resin, but you would need to press it into place since it won't flow (the benefits would be less resin required, and no worries about sealing the cavity so liquid doesn't seep where it isn't supposed to).
2. General case for casting
Pigment vs. dye
The easiest and most effective way to get opaque coloring is to add pigment, rather than a liquid dye. Pigment is any very fine powder that doesn't dissolve or react. There are dyes that can be added in enough concentration to make it hard to see through the epoxy while still keeping it pourable, but nothing you likely have laying around the house, and they don't mask well in thin layers.
People sometimes use food coloring, but that tends not to be color-stable, isn't opaque, and can affect the appearance of the epoxy.
To look like uniform coloring, you need an extremely fine powder. The powder will obscure visibility more effectively if it is something that is actually opaque.
White-looking powders that are tiny crystals (e.g., baking soda, sugar, salt, borax), are actually transparent. Used as a pigment, they will make the epoxy translucent rather than opaque (their index of refraction is different from the epoxy's, so light will still pass through but will be randomized). If the layer is thick enough, that will still obscure what's behind it, but in thin layers, you may be able to make out what the epoxy is hiding.
With an opaque material, as long as the layer is thick enough at the concentration of pigment so the pigment is at least one particle deep everywhere you look, it's opaque.
- Talcum powder is a good, readily-available material (make sure it is talc rather than corn starch, which is often substituted in baby powder).
- Various forms of carbon (e.g., powdered charcoal, lamp black, graphite, etc.) are the go-to black pigment. If you don't have some form of it in a powder, you can make your own from something like pencil lead, the electrode of a dead dry cell battery, or a barbeque brickette, although it may take some work to get a uniform fine powder (luckily, you don't need much).
- Calcium carbonate is often used as a filler (from common sources, grinding some chalk is an easier way to get a fine powder than crushing egg shells).
- Another often readily-available material is mica powder in the form of eye shadow, although that will add a decorative shimmer to the epoxy (it's sometimes used with another pigment to make it look metallic or pearlescent).
- Plaster of Paris might work, although I've never tried it.
- Elmy's suggestion of sawdust can also work for casting, but for that application, it should have a very small particle size and a low moisture content, and a vacuum chamber is usually needed to get rid of the air bubbles.
Small amounts of oil-based paint supposedly can work, but I've never tried that. Acrylic paint is sometimes used. That is pigment in a water-based binder, and water and epoxy don't mix. High-quality acrylic paints that are a paste consistency have less water relative to the pigment. Mixing in small amounts, the negative effects of the water will often be masked by the pigment. It isn't ideal, but it can work. Acrylic paint wouldn't be near the top of my list.
Many household substances that are powders, or can be turned into powders, can be mixed into epoxy. Some will work fine, others not so much. In sorting out what to try, here are a few considerations beyond what has been mentioned.
I would generally avoid:
- Anything that dissolves in water. Some of the particles will end up on the surface. Cleaning the surface, sweat from hands, etc. may dissolve those particles leaving matte areas that affect the appearance.
- Powders that are crystals that dissolve in water. Many of these are "hydrates" (a chemical form that contains bound water). Some of these aren't particularly stable, and break down over time, such as losing their bound water. This could affect the appearance of the epoxy in unpredictable ways.
- Food products. Complex organic stuff can break down over time (often accelerated by UV exposure), change color or appearance, or be attacked by microbes already in it. So the result might not have a stable appearance long-term.
Powders that are mineral in origin other than the exceptions above, are generally safe bets.
You don't need a huge amount of pigment to make epoxy opaque, although it wouldn't hurt if you use more (i.e., it won't affect the epoxy cure or for most practical purposes, its strength or how well it adheres to what you're putting it on/in). In fact, you can use mostly pigment with just enough epoxy to act as a binder since the pigment is cheap and epoxy isn't. It needs to be very well mixed so there are no pockets of pigment powder, and you will want a longer-setting epoxy to give you time to mix it and work with it.
The pigment will thicken the mixture. At just a few percent of the mixture, there won't be too much change in viscosity, and that may be enough to give it opaque color in the thickness of epoxy you need. Adding more pigment, it will turn into a paste consistency. When you start getting to the point where the epoxy is more of just a binder, the consistency will get more like sticky putty or clay (that's basically what epoxy putty and clay is).
As Elmy mentions, pigments can settle. This is a bigger issue when the epoxy is low-viscosity, there isn't much pigment, the pigment is heavier than the epoxy especially if it is not a super-fine powder, and/or the epoxy has a long setting time. Settling isn't an issue with light fillers like sawdust, which Elmy suggested, or carbon powder.
With a mineral filler at clay consistency, any effect might just leave the surface looking glossy rather than matte. At lower concentrations, settlement can be reduced by using more-viscous epoxy, with a gelling time not excessively longer than what you need for working time (it doesn't need to fully cure to stop any settling, it just needs to reach the state where it starts to gel and become very thick). Start with pigment that is an extremely fine powder; that takes much longer to sink.
You can speed up the cure once everything is as you want it by gently warming the epoxy, although that might temporarily reduce the viscosity, so it becomes a race between settlement and curing.
Settling is mainly an issue if you are casting something thick. If you're just making a small amount, like for a repair or to line an oversized hole, it won't be an issue.