are there rentable covered pavilions?

No

There is a gazebo and a pavilion for shade. In the evenings, they may be occupied during scheduled events such as Sunday nights with the Cincinnati Pops or The City Flea. However, most days, anyone can sit and enjoy shade from either. Whether or not it is rentable, I don't know. I'm going to go out on a limb and say probably not as there are just so many people that visit the park.