"No can do" is certainly an alternative to "no dice".  The meanings are quite similar.   I'm impressed with your knowledge of slang. 

Dale, lend me five bucks.

No can do.  I'm flat broke.

And....when we agree to something or want to say that something is possible, we can say "Can do." 

I'm having car trouble.  Can you take me to the garage?

Can do.  Jump in.

Sorry I don't have a prize for you!