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I got the Rooster but when it ask me to place the COOP of course an error popped up and I had to close the window and lost the option to place the COOP.
Clear cache/refresh page or see if coop is in your inventory. Depending on if you just got the mission or completed to get the rooster fully the coop building is just a decoration and would go in your inventory or you would place it on farm if you wanted to
But as said not sure if as said you are just now getting the mission for the Rooster Coop or completed it and got the Coop to keep one that is either place or go to inventory
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Farmville2 Country Escape