P51 is fine.. You can do two things 1) Flatbands (Loads of guys sell them here.. I use Tex's love em!) Or you can try to make them out of exercise rubber from Wal-Mart. 2) Get RRT tubes haven't tried em but pretty sure at 10-15 yards they will kill birds and rabbits. Walmart also carries steel shot too.. It's near the airsoft/paintball stuff. You can use lead balls for hunting.. Musket balls will probably be the easiest for you to get.. You'd have to look.
Flats are faster then tubes, it's why they are popular.. Tubes last forever.. They both have pros/cons I use both.
Currently stalking some rabbits myself.. I found a warren so hopefully, I'll have some photos to share..
You can even buy a bag of office rubber bands and rig em up.. Sir Shot can definitely give some advice there.