You could 'try' cutting a spare piece of skin to glue over the tear as an (obvious looking) patch. I patched an old tambourine that way.

I had a similar problem with one of my banjos. I wet the area down and stitched up the tear with artificial sinew. (waxed linen I use to sew leather bags). And let it dry. 

Worked well for quite awhile. Not much change in sound. Friends would call it my “Frankenstein” banjo. Hopes this helps. 

Thanks, Patrick.  That might be beyond my experience and know-how but I appreciate the suggestion.