Rainbow road is a breeze once you get the hang of each corner. I did 150cc special cup yesterday and got star rank, but for some reason it didn't save, was so annoyed. I did it again and only got an A rank, but I'm determined to get star ranks for all cups ;)
So yeah, practise on time trials for a while to get a feel for the track. It doesn't compare to having stuff thrown at you constantly - but make sure you get every single boost and do tricks on every bump, and don't do tricks up the sides around the two big gaping holes - just cruise past them. Keeps you ahead whereas fancy tricks delay you.