I'd like to build something to put paper targets on that would hold up to being outside but was easy to shove pushpins in.

I've tried OSB and plywood but they don't hold up and they're not easy to push those little push pins into.

I don't think cork would last.  I thought about bead board but I'd bet that won't hold up to wind and sun.

I'd like to have something that was about 4'x4' so I could put several targets on it at once. 

It should hold up to a .22 for a while, I saw one guys plywood holder with about a 2" hole in it but the rest was okay.  So if you didn't blast out too big of an area it should be okay to hold targets for quite a while.