I have to laugh about the standard Public Health type suggestions to get rid of standing water (not in the above post specifically, just ANY time that is suggested) -- yeah, obviously that makes sense, but it does zero to get rid of the nine bazillion mosquitoes that bred in someone ELSE's standing water and are just generally infesting the whole area
Believe me, how much standing water you do or don't have on your property has really pretty much nothing to do with your mosquito count, in an area with lotsa mosquitos!
If you have tall grass or other nonlawn plants within 20' or so of the coop, eliminate them if possible, that will decrease the mosquitos hanging around.
Planting lemon balm or yarrow (large amounts of 'em) helps somewhat but by no means totally IME.
I get mosquitos hanging out in my chicken bldg in the summertime, esp in the darker back half of it, also in my darkish barn; I think they are trying to stay out of the bright drying exposed outdoors? Anyhow, I do know what you mean. If you could get more light and/or air movement in the coop in general and the nestboxes in particular (keeping an eye out for chickens conceivably becoming annoyed by more light), that would likely help.
Spraying a citronella and/or pyrethrin spray on the walls of the coop occasionally can help, but I am personally leery of doing it, I certainly would not do the spraying when birds were in the coop or likely to reenter soon.
Good luck, "have fun",
Pat, in a mosquito swamp for most of the summer
