I agree, no-signup is really nice, esp. since I'm hesitant to have my kids signup for things, and of course free is nice. That said, if you do want or need to monetize, one idea would be to slap a donation link like 'Buy me a beer' on it. I could see some people being willing to send a few bucks to your daughters' college fund in exchange for infinite coloring pages for their kids. Also, it probably makes sense to cache if you're not already - once someone generates "Paw Patrol vs Scooby Doo", put it in CDN and serve up from there instead of generating again.
Maybe "Buy us some crayons" instead? You could even do a partial donation for coloring supplies to a kids' charity.