Synthetic stocks should be dipped (anyone know who does that?)
honestly, I have painted a few wooden and one sythetic stocks a long time ago. Buy one of the 4 color kits from Hunter Specialties and start with the lighter colors, then add the darker ones (tan, green, brown, black). I fyou want to be fancy you can use leaves as stencils, fern and oak leaves make cool traces. Do your stenciling with the brown and green, depending on the season and terrain for best results. Green background for spring/summer or someplace with lots of evergreen and brown background for fall/winter.
Then use the flat non-reflective lacquer coating to protect you masterpiece.