Atm, I'm helping my buddies level up, and I'm setting up rune pages, I play a lot of Gragas, and I'm happy with him. But one problem we have is that we can never find a nice comp that is strong, not relying on one person to be the carry and the other two to just sit there. The only comps we have come up with so far is:

Volibear
Sion
Gragas

However, my buddies don't want to always play the same champions over and over, what do you guys think?

You could try Yorick as your AD, he is pretty good. Pantheon is good on TT also. He doesn't get played enough, which is honestly a good thing for me. Shen is good too.

Lee's a great ad for TT. And getting them started with some skill shots is a good idea.
I don't like new players learning on sion. I did so, myself, playing him the majority of my first probably hundred games - it set me back. His kit is so .... split .... re ap/ad, his stun makes you not really respect positioning, and he's just generally "easy" but not with much transferable skills.

Rumble is a great pick, and someone likely worth learning. Irelia, maybe. Xin is fun and requires some thought. The difference between a mediocre shaco and a great shaco is just silly.

Let them try carry you, occasionally. Pick blitz, and set them up.

I like pairing nunu with some ad, like voli, xin, or trynd

You should counter pick, not every game demands the same cookie cutter team setup. I find Gragas incredibly dependent on their picks, if they've got a team that you need to force away from each other like say a GP or somebody building aura items, then gragas otherwise you run the chance of missing an ulti and hurting your team more than helping. I wouldn't touch volibear either unless their team has some crazy ad carry like Riven, Tryndamere, etc. I would avoid Sion for just about every situation personally.