I have a small (6 inch ish diameter)tree, a 5 foot long segment of rope, and 2 carabiners. How would I make a rappel anchor?

From the rap rings hopefully situated next to the tree.

You could skip the gear entirely and just drape the rope around the tree, but then on pulling the rope you'll damage the bark, hurt the tree, and I wouldn't do that unless it was an emergency.

You didn't specify the circumstances. Is this an emergency retreat? Something you plan on actually doing or just as a brainteaser? That's a pretty small tree to trust your life to, depending on soil and type of tree it could pull out. Why do you only have 5 feet of rope and not any slings? Do you mean cord? You could also tie a loop around the tree (join ends with double fisherman's knot) and put the rope right through there to get the rope over a lip (since rope won't be moving while weighted it's ok, although when pulling it can damage the cord leaving behind tat that someone else might use and then it fails). Or you could oppose and reverse the biners, leaving behind your entire stash of retreat gear.

I guess, in summary, this isn't a great situation, and without knowing more about the context it isn't possible to give a good answer, all my above rambling is rubbish!

You can make a retrievable rap anchor with this gear using a small diameter tag line to pull the anchor back through itself. This is often used in canyoneering. I will NOT describe it....I'll see if I can find a diagram of what I use.

Tie a rope around the tree, connecting the ends with either a double Fishermens knot or a Flemish bend.
Try to get the rope as low on the tree as possible to reduce leverage.

Clip your 2 biners to the rope loop, making sure the gates are opposite and opposed.
Or, if you want to little extra security, take some athletic tape and tape the gates shut.

Assuming the tree is well rooted and alive, you have what should be an acceptable rap anchor.

The maximum force on an anchor when rapping is about 2 Kn or 440 pounds, so the anchor does not have to be superstrong.