We have actually been to a couple of these. Just contact your local children's gymnastics facility and hopefully you will find out that they offer prepackaged birthday parties.
Parents deliver kids to the facility for about two to two and a half hours of fun and tumbling.
The first hour or so is spent on the equipment and the last hour is spent with cake, ice cream and presents. The facility will provide spotters to assist the children as they use the equipment. If you live in or near Plantation, Florida, check out the Mygym Plantation.