Both are correct. The first is just what teachers promote to keep middle-schoolers from disrupting class with "your anus" jokes.
http://www.merriam-webster.com/dictionary/Uranus
That's a myth. Both pronunciations are common enough to get in a dictionary, but the YOOR-uh-nus pronunciation is based on the original Greek and Latin. It's the original, more technically accurate pronunciation, and the idea that it's an invention of joke-avoiding pedants is merely folk etymology. (Besides, is "urinous" really going to be any less amusing to the juvenile mind than "your anus?")
There once was a lady from Venus
Who was known for her sexual freeness.
She would go on a date
With one partner or eight
Irrespective of gender or genus.
I didn't know Dax was from Venus