I've used stain, but be very cautious, it will be darker than you plan. The antlers suck it right up and it's near impossible to get it back out.
I used water based paint to match a fabricated replacement point on a muley and it worked great. I cut it heavily with water so that it was very light then worked it darker. The water based paint holds up fine on the wall indoors. They even make a clear if you want to shine them a bit when finished.