Most standard one diabolo tricks, or some version of them can be done inside a loop. Other tricks can be done which will only work on a loop. The best thing to do is play around and see what you come up with.
Here are some of the tricks that I like - hopefully you'll be able to work out the possibilities by having a go at some of these moves.
You can see some of the tricks described below in this movie (3.23MB). The movie includes some around the hand variations and shows the 'doubling up the string' trick described below.
Around the hand: Instead of making the diabolo go round both hands, you can get it to go around just one hand. There are various variations:
Stopover on top of the string: this is just like a stopover with sticks. Just use your index finger finger as if it was a handstick.
Thumb stopover inside the loop: When you do one diabolo inside a loop string, your thumbs normally do nothing. But you can use your thumbs to trap the string, to create stopover style tricks.
Around arm/leg/head: instead of using both hands inside the loop, you can put an arm or a leg into the loop. The hand that is still in the loop keeps the diabolo moving, and makes sure that the string is still taut.
Suicides: there are all sorts of possibilities. You can take one hand out of the loop and swing the diabolo in a full circle with the other hand. This has a good a visual effect as it changes the size and shape of the diabolos movement. You can also just throw everything in the air - to catch it, you just need to get a hand back in the loop as it comes down.
Doubling up string to half the loop: this is one of my favourite loop diabolo tricks. As the diabolo moves past the left hand, wrap the string around the near side cup. Only wrap the half of the string below the hands, not the half above the hands. If you have slippy string, you can now continue to make the diabolo move around both hands while still wrapped. To get into a double loop, let the diabolo drop between your hands as it passes over the top. You should end up with the string in a V shape made up of two loops. If you move the two loops together, you'll see that you now have the diabolo inside a doubled up loop. Easiest way out of this is to pop the diabolo out of the looop, drop one of the loops, and pull the string tight to get the string back to it's normal length.
Yo-yo style finish: get the diabolo spinning very fast by doing it inside the loop. Pop the diabolo out and catch it on the top of the loop. Next, pass the end of the loop you're holding in one hand through the end of the loop held in the other hand, and let the diabolo pull the knot tight. If the diabolo was spinning fast enough, it will do a string climb, and the string will appear to have disappeared! You now have a little knot to undo, so this is a very definite finish move!. I've had some luck with getting the diabolo to work as a yoyo after doing this finish. It's not very impressive, but it's worth a play anyway!