I was told recently that if you put Vicks Vapour Rub arround the lower trunk and branches it deters them although I have not yet tried it.
Try contacting the DNRE (Dept Natuaral Resources and Env.) I believe you can now kill possums and long as it is done by a vet humanely ( this could be expensive) but check with them.
They may also have other suggestions.
You can buy a possum trap and maybe you have a 'friend' a who is a Vet.