Hi everyone. I've been following this thread since I started playing. It has helped me out multiple times and now I would like to share my knowledge with the rest of you. I'm level 19 and have bred and hatched 2 sun dragons and 1 moon. Of all the "tips" posted so far, I think one may have been true. The breeding and incubation times for both are 48 hours and the eggs look like a checkerboard. I bred all three at 2:30 - 3:00 pm EST. time makes no difference in which you will get.
The dragons I used were all level 10.
Blue Fire + Crystal got me my first sun.
Sonic + Storm got me my second sun.
Sonic + Storm also got my my moon.
Feel free to add me and check it out. GC is same as here: Shavemeshavers. If I can post screenshots, I will.
-EDIT-
I would also like to point out that I did have one sun habitat and one moon habitat before breeding, but I got my second sun before having the second habitat, so that doesn't matter either.
Also, a HUGE tip that I found was do not have boost buildings on the same island as your breeding cave. Not sure why, but it helps to get the breeds you want. My fiancé has been trying for a sandstorm for weeks, I gave her that tip, and 3 tries later she had it.