You get this through informal channels - basically this is just a group of friends where someone offers to babysit the kids free-of-charge one day when their friend really needs it, and then the friend reciprocates, and they each bring in a few more friends that they know are trustworthy, and so on. I'd imagine thousands of such groups of friends exist (I suspect this is the primary form of support in many immigrant communities), but you wouldn't really hear about them, because it's all word-of-mouth through social connections. My wife and I have certainly done this for our friends, though, and it's come back to us.

For more institutionalized settings, there's co-op daycares, but we looked into this and they're largely incompatible with having two working parents since the schedule usually requires volunteering in the middle of the workday.