I am currently applying for a research/study grant, and need three letters of reference. Would it be out of line to ask the recommenders to coordinate with one another so that they don't say anything conflicting, and don't double up on the same exact content? Not sure what the norms are.
It's certainly a good thought to make sure your letter writers don't double up on information to the detriment of their unique perspectives.
However, it certainly sends an odd vibe to ask that they three communicate with each other to do this ... They are doing you a favor writing the letter in the first place, but adding to that to try and make them coordinate with two other professors is a huge load, and plus, if you want three professors to work together, you might get your letters in a year, if they aren't too busy.
That said, it's absolutely normal to talk to one professor and ask her to write about your programming abilities in particular, and to ask a second to talk about how you are a quick study, etc., so that the letters are complementary.
I'd think do not ask them to coordinate. Not that it's such a terrible idea, but that writing letters of recommendation, while arguably part of one's professional responsibilities, is not quite obligatory, so has a component of "doing a favor". In that context, to ask for coordination would be adding (possibly considerable) work, since academics are not known for their cooperation. E.g., I myself will invariably write letters, but if I were obliged to cooperate with colleagues not of my own choosing, I might balk...
Anyway, "doubling up" on content is confirmation.
If there is "conflict", well, why would there be? As a long-time reader of recommendation letters, it does not surprise me when people have different opinions, or even different recollections of fact.
So, also, I think don't worry about those issues.
EDIT: To be clear, it's not that I imagine myself to be uncooperative (probably no one does!), but that my experiences with colleagues have made me dread most "cooperative" work. That is, I'd rather do twice (or more) the work than have to "coooperate" with randomly-chosen people. Certainly other people may feel otherwise, but asking for cooperation is asking for more, and perhaps quite a lot more work than you'd anticipated. Thus, since I think there's little if any to be gained... just let it go.