Though I'm not into Russian made rifles - real or replica - it is my opinion that they look just fine the way they are. I would think that, should your rifle have real wooden furniture, it would look better the way it came. If the furniture is plastic, I'd say paint it all black. That would look meaner than anything else.
Keep in mind that the Dragunov rifle isn't necessarily a sniper weapon. It falls under the same category as the M14 or SR-25. It's considered a DMR (Designated Marksman Rifle.) A camouflage paint job isn't necessary or befitting these rifles. (Though there have been times when the carbine based models have been painted.) This rifle is more likely to be painted due to the overall attachments desired by many American soldiers who, in the heat of battle, are working alone.
In close, my opinion is to leave the wooden furniture wooden - re-stain if necessary - and paint plastic/ABS furniture flat black. But, that's just my opinion. (Leave the metal parts of the gun a semi gloss though. Only paint the furniture. Then beat it up a bit. Put some wear and tear on it. Make it look used a bit. You don't want your rifle looking like a cherry needing to be popped. A worn rifle looks more dependable and intimidating than a new one.)