Yes, both "try" and "go on" are acceptable ways of saying that. You can use 'ride' for each of them. Ride the roller coaster, ride the merry-go-round, etc. Another verb for bumper cars could be "drive." I want to drive the bumper cars. As well as "crash." I want to crash (into you with) the bumper cars. For merry-go-round and ferris wheel the verb "spin" also applies. I want to go for a spin on the merry-go-round. I want to take a spin on the ferris wheel. As for other common rides, I haven't been to an amusement park in a few years so I'm not too sure what's common these days. Anyway, I hope this helps!

Hi Apple, try and go on are good for these sentences. You can also use ride as a verb and say, "I want to ride the roller coaster." Here is a page with many amusement park rides: https://en.wikipedia.org/wiki/List_of_amusement_rides