If you can, tear it down. If not, mask the "business" parts really well. Don't get any paint on the string/ cables, cams, axles/ bearings, etc. Then just hit it with dull colored, non-reflective paint. Krylon would be fine.
It's an old-school practice; from times when camo bows weren't the norm. Just check out pictures of Randy Ulmer. He's old-school, and his bows show it. Lots of his rigs have obvious splotches of OD greens, browns, and tans. The guy could likely get any bow he wanted for nothing and even the camo bows get tagged...he must believe it gives him an edge.
The new paint may not wear to well on some surfaces, but dulling shiny parts and adding some color would be achieved. I haven't done a bow but all my stands, ladders, and other hardware get paint. I have used the Krylon Camo and the Rustoleum Camo paint seems really good too.