Greg, you're probably looking for a calfskin head. That's not the most traditional (possum?), but it is close enough and easier to find than other skins. If you get up to the DC area, you could call the House of Musical Traditions in Takoma, where they are used to dealing with folk instruments. I bought a calfskin banjo head from them a while ago, which means they at least used to have them in stock.

Somewhere in my back memory is a comment from someone that cat gut makes good strings, that the neighbors felines are always up for grabs for this purpose, but that it is unneighborly to take your neighbor's last cat.

Having shared houses with many cats over the years, I do not endorse the above.