Hi there, Thaliafan! From my native instincts I would normally say that it's : Часы с кукушкой. (chasy s kukushkoi) but apprantly, according to my big dictionnary, it is translated as: высокие стоячие часы. However I have to say that I have never heard it being referred to in this way, and I would never myself call it that..
Не за что. It's actually plural - часы. (они) And you never get it in the singular form when you're referring to a clock/a watch.
But you do have the word час which simply means an hour, and is masculine.