I painted the stock on my Marlin 880SQ, which is also a synthetic.
I figured it must be some form of plastic or polyurethane , so I painted the first coat with Krylon "fusion" paint (made to bind with plastics)
Then I followed with krylon camo colors.
Other paints may have worked as well but I find that applying Krylon paints over others can produce a crinkle finish (different reducers), so I didn't take any chances.
...Anyway, Krylon does have some nice, flat camo colors...available at Wally World...