A couple of weeks ago my wife and I visited our friends with two kids who have the above mentioned trampoline put up in the garden. It's lots of fun for kids and even adults might be tempted to give it a try but watch out not to fly over the boundary of your property into the neigbours hedge
Luckily the neighbours next door have kids in similar age and both families understand each other well on the same wavelength.

As far as such installation is concerned, it's not permament, it can easily be disassembled and as long as it isn't on the neigbour's property, I will not see any legal issue unless the noise generated by fun and joy affects the elderly generation, but only in specific hours defined by the law.

I would invite your friend over, host him with some wine or beer and let him/her have a few "up's and down's" on the trampoline. Maybe he/she will change her mind. Good luck