Well, I know this one, cause the show was one of my favorites! It's called "Journey to the Unknown" and was originally broadcast on prime-time ABC during the 1968-69 season. The first episode was entitled "Eve," about a mannequin that comes to life (played by Carol Lynley). This particular episode inspired an early Carpenters song, also entitled "Eve."
"Journey to the Unknown's" opening credits were in an abandoned amusement park (at night). The viewer ended up on a roller coaster, as an eerie theme song (sans vocals) played.
Incidentally, "Journey to the Unknown" was produced by Hammer Films, out of the UK. They're famous for "Horror of Dracula" and "Curse of Frankenstein," both starring Christopher Lee and Peter Cushing.
Ah...my old brain has been put to some good use!
Rod