I can't say I know how to deal with such issues, but it seems to me that the reasonable thing to do is to avoid moments where it is obvious that you are plotting by convenience. If you say "Oh, well if I just do this, then I can put these characters together, and then everything I want to do can be done," then it seems to me that you're dealing with convenience. Worst yet, it makes no sense to a reader why you wouldn't just put those characters together in the first place if you wanted them there anyway. There are factors that make all this obvious; rapidity is one of them. The quicker you try to make your plot happen, the more clear it is to the reader that that is what you are trying to do. The nasty critical side of me wants to point out that this is amateurish; I've done it, and where I see it I know that I have done something terrible.
Having said all of this, I have no advice whatsoever on how to avoid it. Like I said, I still do it from time to time. The only thing I can think to do is to ask yourself at every plot turn if you're using convenience rather than logic. If you are, then you probably should think of something else. If you know that someone is going to say "this is terribly convenient," then it doesn't make sense to continue going in that direction.
But, I want your opinions on this. How many of you have experience this either in your reading or your writing? Let me know in the comments!