how can we politely invite the adults but tell them to leave the kids at home with a baby sitter?
I have been on both sides of this question. We are younger than many of our friends, so they had kids when we were just in a couple-only phase. Now we have kids and our friends' kids are grown and long gone.
Many of the answers here have some good ideas. But I would suggest NOT giving reasons (breakable items, food everywhere, etc.) since I think they can engender bad feelings. The reasons also can prompt delusional thinking: "Well, it's OK if we bring our darling Esmerelda, because the hosts said they don't want the added noise / said they have breakable items. Darling Esmerelda is NEVER noisy and NEVER breaks anything, because she is so perfectly behaved! She's practically a grown up even though she's three, likes to destroy furniture, isn't potty trained, won't eat unless hand fed standing up and only screams for 50 minutes of every hour!"
Instead, invite the friends for a special grown-up evening. As others have said, give plenty of notice and provide some additional cues that this is a special, one-off evening. Do this by:
Sending an Evite.
I don't know how you normally arrange these events, but Evites are free and you can pick a suitably adult-looking invitation. As @Mast notes below, the Evite should explicitly say, "A grown-ups-only evening at the Smiths" or something else that lets guests know to leave children at home.
Picking a later start time!
You don't say what time these things usually start, but if you are the host, you should be able to pick the tone and time. If you start your event at 8 p.m., when most kids are (should be)in bed, that's a giant clue to reinforce the "grown-up" dinner to which you have already alerted your friends.
Choosing a "grown-up" theme/food.
Pick your evite accordingly and note "an evening of X cuisine" with X cuisine being something specific and not necessarily child friendly. You might also choose to change the attire -- just for fun, ostensibly, but also to reinforce a "grown up" ambiance. This doesn't have to be a 1950s costume party, but you could write "cocktail attire" on your evite.
I think the key to making this evite/evening fun for your friends is testing the waters ahead of time. You can call or email the group and say you wanted to mix it up a bit, celebrate the group, whatever and want to do this by doing something different JUST THIS ONCE. "What does everyone think about a kind of grown up cocktail party? We'll start it later, make it adults only, etc. etc." You might add how much you love being around such amazing, wonderful ... spirited ... children but thought that it might be fun for the parents to let loose and not have to be watching anyone else.
I think the right email preview of the type of evening you envision could help prevent questions and hurt feelings when guests get the Evite.
Lastly, if one or another couple in the group is so tone deaf as to ask you if you really mean that they should leave THEIR darling child at home, try the following:
"Of course we always love being with your amazing Hubert! He really is an exceptional 4 year old! I never knew a child that age could so easily destroy, I mean be so creative with his crayon additions to, our fine art collection! But you know, we couldn't accommodate all the children in the group for this one evening. (Just between us, not all the kids are as precocious as Hubert!) So we wouldn't want to hurt anyone else's feelings by including Hubie after telling the others to leave their children at home. I'm sure you understand the tough spot we would be in if we included Hubert, even though he, well, um, stands alone in his behavior."