Acrylic works great and is about the easiest paint for this purpose, but.....it looks like acrylic paint. Depending on how authentic you want to go. I really like the look of earth pigments, which are pretty inexpensive, but are much more work to use depending on what you use for a binder. I've used hide glue, shellac, egg yolk as binders, and prefer shellac, but have never used it on anything flexible, just arrow cresting, but have used pigment mixed with hide glue for bow back, which works great. As far as how well this will bind with your previous coatings of tung oil, I'm not sure.