There is nothing safe you can do to keep a pool clean. My dh is a biologist with a specialty in aquatic toxicology, so I say this with some expertise. Unless you were adding chlorine or bleach to it, which is bad for baby, then there is still going to be algae, dirt, body oils, urine (possibly) and other bacteria in it not matter what you do. Covering it is just going to create a petri dish for bacteria and algae to grow. Leaving it uncovered is going to let in more detritus.
We do not use our baby pool every day but when we do, we make sure it is clean. If dd is playing with it all day, we may pour out the water at least once and put more in after a quick hand scrub with the hose. We do not use our pool every day because water is expensive here.
Hydrogen peroxide and vinegar would both be nasty for baby's body. Just dump the pool daily, give it a scrub, let it air dry completely, and don't use it daily if water is expensive for you.