Try oiling the skins to tighten them and keep out the moisture. The theory is that if they were taut when they were dry then driving out the moisture should restore them to their original state.

Olive oil should do, or baby oil or even hand cream at a pinch anything which is going to waterproof the skin. Just apply on both sides and leave, after a day or so apply more if the skin has soaked it all in, or wipe off the excess.

If that fails then take off the skins and wash them in warm soapy water- to counteract the oil, and they should go soft and stretchy. dry them off slightly between sheets of kitchen towel so they are easy to handle.

I would thread loops of cord through the original holes like the spokes of a wheel and draw them just taut on the open side of the tamborine using a tourniquet. Allow the skin to begin to dry out and slacken the cords if they pull the skin too tight - that would make them thin and tinny and likely to split.

When you are happy with how the head sounds you can put the tacks in and remove the cord.

Anne