I want to fully paint SD cards in mass quantities, but my problem is trying not to paint the pins in the process. What would be the most effective way to cover them or go about this.
More details regarding your objective would be useful, but one can expect certain commonalities irrespective of your final goal.
First off, unless you are inclined to excessive labor, expect to not-paint the area of plastic between the contact areas. More on this later in the dissertation.
The easiest way of masking out the contacts is just that, masking tape. Consider to use some of the new-tech tape which uses a liquid-absorbing powder to increase the tenacity of the tape edge to repel paint. One brand name is Frog-Tape™ although I expect others are available. You could align the cards in a simply-made jig and run a strip of tape over many at one time.
The above suggestion is valid if your intention is to paint the cards in a single color or a multi-color scheme of reasonable simplicity.
As with many painting tasks, masking is key. If your project is simple shapes of various colors, creating a mask for each color, with spacing to match a jig holding the cards, you would be able to apply the paint in sequence, alternating masks and spraying.
Consider the following: your image is the common yin-yang symbol, two colors and a neutral background.
Mask the contacts as noted above, which would also secure them in the jig, and apply the neutral background color. It is critical that this base color be allowed to dry thoroughly, to prevent peel-up from the following steps.
Your masks would have to be created from an adhesive material for best results. Vinyl sign material comes to mind, although you may get away with wide masking tape cut on a hobby cutter. Using transfer tape, the mask is applied to the jig containing the cards, leaving opening for the desired color. The masking is removed when the paint has become tacky, but before fully cured, to prevent peeling at the edges.
Repeat with the second mask and the third color.
The tricky part for multi-color designs is registration, also known as alignment. You would want the jig to contain clearly visible points to match up with mask one and mask two.
Silk screening uses similar concepts for multi-color, although the contact masking would be simpler. The screen has openings for the ink to be applied and is solid in locations of no ink. Photo-sensitive screens allow for accurate and easily created masks for simple artwork such as the symbol. The construction of the silk screening platform usually includes registration/alignment if done properly.
The area between the contacts could be painted using the silk screen method and even possibly using the vinyl cutting mask method, but requires very careful attention to registration as well as mask creation. Considering how small those areas are makes it a better idea to leave them in the original state.
The precision you engage in creating the jig will make the rest of the task all the easier. One could consider a 3D printed jig or perhaps laser cut acrylic. Laser cut plywood may be practical, but the organic nature of wood makes it susceptible to humidity and temperature changes. If you have access to a CNC resource, aluminum or acrylic becomes practical for making accurate jigs.
As the pins are recessed I'd first try pressing that side of the card against a thin pad (even just a thick cloth on a board). Two coats would be a good idea. That will get you a solid colour, and I assume that you need solid colour if you're talking about mass quantities -- if you can paint a design you can paint precisely enough to avoid the contacts.
This at least would provide a test method; it's quite likely the the paint will scratch off in some places in many devices after only a few uses (which might or might not matter depending on your goals).
For repeated designs, stickering may be better, or stickering over a painted card. For larger quantities getting it done for you (first hit on my search, even Kingston will do it from 500 units) would be an option.
If you do want to paint the bits between the contacts, then you might try experimenting with watercolor masking fluid. It's a rubbery compound that you paint on and allow to dry before painting. You'd want a small flat brush just the right size to cover the contacts with one stroke. It peels off completely, and I don't think it would hurt your contacts once removed. My favorite brand is Pebeo Drawing Gum because it's easier to apply with a high degree of precision than other brands I've used.
The only thing I would be worried about (assuming you can apply it easily and quickly enough) would be how it would work with whatever kind of paint you'll be using. You'd want to experiment with that before working on something you care about.
Consider printing on thin translucent film and die-cut the stickers that can then be transferred to the SD card. This will completely avoid the need to mask the contacts. This occurred to me because I have been working with Epson TM-C7500 label printer that is full color and has pretty high resolution. However, any ink-jet or even color laser can be used with suitable film stock. There are printable films with adhesive backing. Simple die-cutting machines are in price range of desktop printer but I have never used one. Here is one example: Cricut Explore Air 2 Mint
If your SD card is made of black plastic but you want it to be pink all over, then it may be more cost effective to obtain pink cards.