My first question would be, are you sure the water isn't coming up from the ground? (If your coop is raised on blocks with a raised wood floor, it isn't, but if it has a dirt or slab floor then that's by far the likeliest problem... see my 'muddy run' page, link in .sig below, for ways to direct water away from coop)
If it is a raised floor, then either you have a leak you don't know about (e.g. sometimes water can track down inside of a hollow wall) or you need more sanitation or more ventilation. (Humidity makes stink a lot worse, so it is not difficult to have a situation where the coop seems ok in dry weather but on rainy days it is all smelly).
To the extent that your problem relates to water coming in the popdoor or in on chickens feet, you can build a little 'porch roof' over the popdoor, and put a cinderblock or paver or whatnot as a sort of doormat so the chickens are not going directly from a puddly run to the bedding.
Good luck, have fun,
Pat
