There are no studies out there that say amusement park rides, including roller coasters, bumper cars, the Whip, etc., are dangerous during pregnancy but not many women are willing to be in a study to see if repeatedly riding Kingda Ka at Six Flags will cause them to miscarry.
The concern is with the rapid starts and stops and jarring motions that occur with these types of rides which could lead to premature separation of the placenta from the wall of the uterus.
Honestly, from everything I've read, it seems pretty hard to knock something loose that wasn't going to knock loose anyway but amusement parks and doctors aren't willing to risk giving you the green light then have you sue them if you miscarry.
So until we get a bunch of women saying "Sure, I'll ride the bumper cars for a week straight to see if my baby survives" you're SOL on the side lines holding everybody's bags while they ride the Tower of Terror.
Might I suggest picking through their wallets and getting yourself cotton candy? It's not an amusement ride but it is amusing.
search: amusement park pregnant, carnival rides pregnant, roller coasters pregnant, bumper cars pregnant