If you want to tarp it, just get a tarp with those round holes around the edge, and use bungee cords to attach it to your deck and stretch it taut. (In the yard, use tent stakes -and bungee cords if needed) to anchor the tarp in the ground.
How deep is your kiddie pool?
I have found that a hard plastic pool (ours is about 4 feet diameter) is WAY easier to clean, doesn't puncture like an inflatable and is easy and cheap to replace if it somehow gets broken. We keep ours empty at night most nights to cut down on mosquito breeding, and when it gets dirty, my son loves to scrub it with a hard bristle brush; he calls this a "water game" and it is just as fun as playing in the pool any other way. We only ever have it filled a few inches, so it is easy to dump out and start over fresh. Your 3 year old might enjoy this as much as what you currently have if you decide to switch over. I have found that cleaning our hard plastic pool never takes more than 5 minutes; usually only 2 or less. When we empty it, we put my son's outside toys in it to hold it down on our deck, and then store it under the deck in winter.
Happy water games to you!