He said he witnessed a goat mating with ewes on his farm during "tupping" season five months ago, but had given the matter little thought until the geep appeared,
He said the new arrival had created a lot of laughter in the pub, when he showed mobile phone pictures of the hybrid to his customers and friends.
"He's an unusual character," Mr Murphy added, saying the animal was developing a set of horns on its head.
The Irish Farmers Journal said it was the first time it had reported the birth of a healthy geep in Ireland.
A spokeswoman for the Ulster Farmers Union said the live birth of a so-called geep is a very rare event and they are not aware of any currently in existence in Northern Ireland.
She said this form of cross-breeding, on the rare occasion it does occur, is likely to involve a buck goat and a ewe.
However, the geep usually dies during the ewe's pregnancy or is stillborn.