The danger from trampolines is not from jumping. (They can jump 'till the cows come home.) The danger is from falling off or climbing off improperly. Strains, sprains, head and neck injuries are a lot more common than people think. Here are the general guidelines:

Use safety nets and pads.
Go ahead and install a trampoline enclosure net to surround the trampoline

Cover the trampoline's springs, hooks and frame with shock-absorbing pads. This is no joke. The money you spend on pads and nets will save you the same amount in bandages and doctor visits.

Place the trampoline on level ground.
If you let them, kids will jump from trees (or houses) onto a trampoline. Prevent this at all costs. Also, try to place the trampoline in a pit so the jumping surface is at ground level.

Limit trampoline activity.
Allow only one person to use the trampoline at a time — and never without supervision. Don't allow kids to practice risky moves like flips. That is what gym classes are for. They have safety harnesses and insurance.

Discourage unsupervised jumping.
Don't even install a trampoline ladder, which could tempt young children to use the trampoline alone.

Our children have a small trampoline in they use. It has a handle on it to hold on to and does not let them jump very high. We do limit the amount of time but they both can calm themselves by using it

I agree with MyZett. I just want to add that if your child is fixated on the trampoline it is going beyond therapeutic use into stemming behavior. Setting time limits with the goal of elimination would probably be best. I was advised early on to turn my granddaughter's stemming behaviors into useful actions. She used to tap toys on the corners of tables, chairs, etc. I'd say, "Oh what fun! Let's make them JUMP!" We'd do that for a while then I'd distract her and redirect her into doing something else. When she fixated on ceiling fans I'd turn them off. I'm happy to say she doesn't engage in any self-stimulating behaviors today. Even her Echolalia is improving. It is only apparent when she feels insecure or stressed. For example, when someone bombards her with questions as people are prone to do with small children, "What's that? Is that a new doll? What's her name? Did you get her for Christmas?" I stop them and say, Please give her a chance to answer one question at a time. Excuse my lengthy and somewhat off topic response. Hope all this is useful. I really just wanted to caution you about stemming on the trampoline.