Most umbrella insurance policies will cover trampolines although when you do have a trampoline your homeowners insurance will usually be much higher in cost than a home without a trampoline.
Trampolines can be dangerous and it's possible for even a neighbors kid to get hurt on your trampoline so if the neighbors kid or the friend of your child gets hurt on your trampoline it's possible for the parent to sue you in court for the hospital bills related to the child's injury on the trampoline.
So it's important to have an insurance policy that covers trampolines.
Check with your insurance coverage policies to be sure that they cover trampolines but if you have an umbrella insurance policy with your homeowners insurance or renters insurance then most always they will cover the cost of injuries due to trampolines.