What roofing are you going to use. For shingles you really need at least 3/12 pitch (that is, three feet of rise for every 12 feet horizontally) or you can get unsolvable leak problems. For other roofing materials, anything greater than 1/12 is generally at least marginally-ok.
If you are wanting to promote snow sliding off, I'd suggest using either metal or polycarbonate (the more-expensive type of plastic roofing) at a 3/12 or 4/12 pitch. You can go steeper but it gets to be more expensive (more materials) and wind load becomes more of an issue, especially if this is a coop on blocks rather than on deep-set poles or bolted to a proper foundation in the earth. Personally I would not go with steeper unless I were in a serious snowbelt area AND the coop was sited such that it was likely to catch extra-large amounts of drifting snow on top, e.g. if it is in the snowiest part of the lee of a taller barn or some such thing.
Whatever type roofing you settle on, for heaven's sake look up how to install it correctly, it seems like the majority of BYC coop roofs are incorrectly done (especially corrugated plastic) in ways that can seriously compromise not just their leakproofness but their structural integrity and their likelihood of staying put in high winds. Metal and plastic roofing panels' manufacturers produce pamphlets (at hardware store or online at the mfr's website) that give you all the specs of how to support and install the things; for shingled roofs, get a good DIY type book and follow ALL the instructions, not just the convenient ones LOL
Good luck, have fun,
Pat