Personally I don't think you can make other people reciprocate. I think if you invite someone over you really have to do it because you want to, not because you are expecting them to return the favor.
That said, of course I think it's polite for them to reciprocate. And I don't buy some of the comments from other people who say they can't reciprocate because of their home size, dogs, etc. I think then they should be making an effort to take the kids out - either to McDonalds, to play in the backyard, to the movies, etc.
I too have been in a situation where it's been hard for us to reciprocate immediately...we have had a sick baby. I have let the other parents know that we WILL have their child over, however due to the newborns' needs, we weren't even having FAMILY over right now, nor going out ourselves. The parents were very kind and said it wasn't a problem. So I have been keeping a list of who we "owe" a playdate to. Since then I have systematically been going through our list and inviting children over in the order we received invites...sometimes it has been for a playdate, other times it has been to go out. If for some reason that's not an option, I think there are other ways they can "make it up" to people, like driving both ways to Boy Scouts or a soccer game.
So in answer to your question, I don't know of a nice way to go about it. I think the best you can do is if/when you see the other parent say something like, "We really need to get the kids together." I have also contacted friends' parents directly simply saying that my child would like to have a playdate. I have found that usually the other parent is willing to pick up if I drop off, or is open to having the kids at their house without much prompting.
I like the idea of inviting the kids back whose parents DO reciprocate. I think it sends good message.
I have always been one to invite kids over. So now that we needed a little help this year, I don't feel bad being on the receiving end. I know that we'll make it up to our friends and also that we'll be there for friends when they need us too.