The Oxford English Dictionary says:
Murphy, n. colloq. Now rare. = Morpheus n. Frequently in in the arms of Murphy: asleep.
Morpheus was the Greek god of dreams; hence a metonym for sleep. The OED's citations include:
1750 T. Smollett Roderick Random (ed. 3) I. xiv. 110 When Murfy sends his puppies to the heys of slipping mortals.
1823 M. ...