Hi I need some help with getting rid of possums

We have a huge plum tree in our yard which the possums like to inhabit at
night and we are at our wits end. They fight and carry on during the night
and our footpath and front lawn is COVERED with poo and it stinks. You
cannot walk on the lawn or footpath without your shoe getting covered in
poo.

I have read a previous thread about detering them, but we actually want to
get rid of them and the only way to do that is kill them (preferably
humanely). Shooting is not an option as we are in a residential area. Can
anyone give some other suggestions as to how to do this?