Adobe AIR, which can run on Android 2.2+ devices can use a (fledgling) technology called Adobe Cirrus (used to be Stratus) which makes p2p possible.
If you would prefer to use Java and create your own p2p system, you might like to take a look at this project: peerdroid
However, I don't have any experience using either of these on Android, and you are likely to encounter issues, especially if it needs to work reliably behind NAT routers.... Good luck!
I should also point out that it would be way easier, simpler and (unless your app is huge or very special) - cheaper, to do this the traditional way, with a server in between.