Since chicken coops offer 20 chickens at 8 coins per chicken in a 24-hour period, with no cost aside from the initial 5,000 coin purchase of a coop, one could easily cram a farm full of maxed out coops making 120 coins a day, with no need to plant, or plow, or grow. It could essentialy break the game. Same answer applies to Dairy Farms.
The above is only partially correct. When you do the math, it would take 42 days to recoup your money per coop or barn. Especially when you consider the logic of only one coop compared to unlimited dairy barns.
The MAIN reason why there is only one coop allowed per farm is that Chickens in a Coop--unlike cows in a barn--can also give "MYSTERY EGGS". These eggs can potentially be much more valuable than a whole farm of animals.