I am looking to decorate one of those “Yeti” brand insulated coffee cups for my brother for Christmas, and I am not sure what to use so that the decoration does not wash off. I have researched a bit but have only found tips for porcelain mugs, and the surface of this cup is more like a lacquered enamel. I will tell him to hand wash but expect that he will want to occasionally use the dishwasher to clean it. Has anyone had any luck with decorating on this type of surface and having it hold up to a lot of touching and washing? If so, how did you do it? Thanks in advance!
You can fire artwork on porcelain and it will be permanent. Pretty much any other surface won't be. Even commercially applied artwork wears off and washes off eventually.
If you know the actual surface material/finish (like by contacting the manufacturer), you can optimize the decoration for adhesion and durability.
You can protect the decoration by building up a thick coating (via many light coatings) of a clear finish of some kind over the decoration. A protective coating also makes optimizing the decoration material less important. I'm not familiar with that particular cup but if the protected surface extends to the lip you drink from, the coating should be food-safe.
If the coating starts to wear off or gets scratched or chipped, you could reapply it or touch it up while the decoration is still intact.
I haven't tested how permanent it is, but I hydro-dipped a variety of cups, including some stainless steel cups.
What I did, after taping off the sections I wanted to protect, is to spray on some primer geared for metals. Once the primer was dry, I dipped the cups (I used spray paint floated on water), took off the mask tape, and waited for them to dry. Then I retaped the cups so there was a small amount of non-painted surface visible and sprayed on a clear coat. I wanted to make sure that the edge of the paint was protected and there wasn't going to be a large cliff of paint that could catch when using or washing.
So far, I haven't noticed much chipping, even on the glass cups I did, although I haven't actually used them. I have them wrapped for shipping, if I sell them or send them as gifts.
You can also use a laser cutter to etch in a design. Some lasers allow for etching directly on the stainless, but others need a material that's similar to powder coating once hit with the laser. The laser can also burn off the existing paint very accurately, if you don't use too strong of a setting.
Some examples that I could easily find. I'm not advocating brand or retailer.
If instead you choose the stainless steel finish mug you'll know what the surface is, and be able to choose a paint. The others may well be powder-coated (and baked) rather than enamelled.
With stainless I'd use paints intended for exterior metals, bought more as building supplies than craft supplies. Unfortunately tins will be rather large, and colours limited. I would plan the design so food/lips don't touch the paint. Another option is car touch-up paints. They often have an integral brush, but a bad one, and they don't apply very evenly even with a better brush.
All these paints might work on the coating, but may chip rather easily. The problem is you can't really check, unless you want to make a prototype for yourself and treat it rather roughly. But that's also true on my commercially-produced enamel mugs.