Awww! As much fun as it is to paint rooms colors, white/tan walls can be pretty too!
We lived in an apartment when my oldest son was born so we couldn't paint either, the walls were white. The carpet was neutral.
I just picked out his bedding and valance and got a matching self stick wall border that we could peel off when we moved. It was easy and didn't harm the walls.
I remember I also bought a little white bookcase and dh cut out two of the designs from the border and put
them on either side of the bookcase, it was so cute.
We also had a blue glider rocker and a pretty lamp on his dresser. It wasn't completely all done up to exactly match but it still looked beautiful.
I am sure whatever you pick will look great! There are lots of bedding sets with neutral colors so you could either go that way or pick something with color and then accessorize with a colored lamp shade or drawer knobs...lots of thing to do!
Good luck and show us what you decide!