Make an extended roof over hang out of 2 x or 1 x wood, cover with flashing and attach to coop. The flashing could butt up against the coop and sit just below the shingles, so the water will run off the shingles onto the flashing and over the vent. I don't know if I explained it good, but this is what I would try. My attempt at making a sketch isn't the greatest, without using a different method.
l attach both sides to outside of coopl
l attach this board to coop back wall l
l----------------------------------------l
l ^^^^^^^^^^^^^^^^^^^^^^l
l ********* overhang ********** l
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