If you can find a compliant material that will strengthen the rim of the holes you will stabalize the stresses, eg the glue they sell for soles of shoes. But a patch (in leather) will be better. Ask a bodhran maker to give you an offcut of goatskin - I doubt they have much use for the waste. Gurt Mint (Bristol) or Marcus Music (Newport) get to several festivals like Chippenham (they made my bodhrans). I doubt there is too much urgency. If the hole is not where you put hands a repair will last for ever.
I have seen masking tape over tears. Don't leave the drum in your car - or put the car in the shade - don't forget the sun moves! One guy I knew heard his drum go ping from outside the car and his baby hole had become a teenager and was giving him GRIEF.