Once you can do a few suns, you can start linking them together. Here are a few examples of sun combos:
Right then left (1.7MB) - A right side sun immediately followed by a left side sun.
Figure of 8 sun (2.2MB) - If you do a sun in front of your hands, you put a twist in the string. If you do a sun behind your hands, you also put a twist in the string, but it's the reverse of the first one. This combo works by doing the same number of suns in front of the hands as behind the hands. You'll notice that I also did a right side sun in the video - those have no effect on the twists in the string, so you can do as many as you feel like.
5 way sun combo (2.4MB) - My favourite sun combo. This one is quite easy with one diabolo, so it's worth going back to one to make sure you understand how it works. It includes a right side sun and a left side sun, but would work without them. But including them helps to slow things down - you don't need to turn so quickly if you do them!