Looking at both of the methods outlined previously, I've come up with a theoretical way of tying the wet skin on the rim that might be simpler. If you've cut a deep routed groove around the bodhran rim, then the following method should work, although I haven't actually had the opportunity to try it.
1. Prepare the skin as outlined in "Mounting the Skin - Method One" then drape the wet skin over the rim so that the edges hang past the routed groove. Don't leave any slack in the skin.
2. Place a smooth rope, plastic insulated wire, leather cord, or skipping rope into the routed groove and tie it tightly so that it's holding the skin in place on the drum (straight telephone wire would be good for this). Allow the skin to dry. The cord should prevent it from slipping too much. If the skin dries too tightly then simply remove the cord, wet the skin and try again. Add a little bit of a sag to the skin this time. If the skin dries too loosely, place the skin on more tightly and check that you are tying the cord tightly.
3. Once the skin dries the way you want it, you can remove the cord. The skin should retain its shape on the rim. You can then proceed to steps 3 & 4 in "Mounting the Skin - Method Two".