From what you say the use of a patch as above is almost certainly your best bet. If you can't get copydex then any latex or rubber based glue should do just as well as it will vibrate with the rest of the skin more easily.

Go easy on that dubbin! it will make the skin heavy and soft and if it gets wet it will retain the water. If you keep the bodhran in a case its unlikely to get soaking wet anyway.. In order to avoid wear rotate the frame round a spoke from time to time during a session and beat over the whole skin (you will get some tonal variations particularly if the skin is of uneven thickness by playing closer to and farther from the rim)