How can I prevent water buildup in a pit for a trampoline?
As long as she doesn't lower the frame of the trampoline itself, then she's fine there. Any kind of wall should be within the diameter of the trampoline frame or very close to it, nothing closer than the frame's inner diameter &amp; nothing beyond the frame's outer diameter. Eliminating fall off &amp; reducing overall fall height is good. But, many trampolines come with retention nets.

You're precisely right though, digging a pit for it will collect &amp; hold water. She'll need to pump water out or install a catch basin that's piped for immediate drainage. If she can cut it into a downslope or hillside, then the pit must drain slightly downhill &amp; out of a the backside or have an open trench outlet dug or a large pipe poked through any remaining hill.