I make rice pudding with rice milk.  It seems to work ok.  It doesn't
have quite as nice a texture as regular, but it hits the spot for me.
I use a little nut butter to make it a bit creamier, which seems to
help without significantly altering the taste:

1 cup cooked rice
2 cups Almond mylk (or plain rice milk)
1 Tbsp Cashew butter or other nut butter
2 eggs (I use egg-beaters.  Other egg substitutes may work)
1/2 cup sugar
1/2 tsp vanilla
1/4 cup raisins, plumped
sprinkle cinnamon

simmer the rice and "milk" together for 5-10 minutes.  Add the nut butter.
In a separate container beat the eggs, and add the sugar, vanilla, raisins
and cinnamon.  Mix in the rice/mylk mixture and pour into a greased (use
non-dairy margarine) 2qt caserole.  Sprinkle a little more cinnamon on
top.  Bake in a 350 degree oven for 35-40 minutes.

note: Almond Mylk is a rice and almond "milk"

Let me know how you like this if you try it.

--Robyn