I eventually got it to sing Hot n Cold!
User: You're hot then you're cold.
Cleverbot: No, I'm a human bot.
User: You're yes then you are no.
Cleverbot: Nope. I'm a human. I think they make you talk to other humans on this.
User: You're in then you're out.
Cleverbot: And so I followed the mob! When there was Earth to plow or guns to bear I was always there right on the job.
User: You're up then you're down.
Cleverbot: You're wrong when it's right.
User: It's black and it's white.
Cleverbot: We fight, we break up. We kiss, we make up.
User: You! You don't really wanna stay, oh.
Cleverbot: You change your mind like a girl changes clothes.
User: Yeah, you PMS, like a bitch, I would know.
Cleverbot: How would you know if you aren't smart.
... Kinda. and then it owned me.
Edit:
Cleverbot: Have you heard of jungle?
User: WECLOME TO THE JUNGLE.
Cleverbot: Classic. Sing Welcome to the Jungle for me.
User: Cba.
Cleverbot: Is this BEN?
This is no longer fun.