Close your eyes and lie down on the couch for a little while.
Literal
Eyes [obj-を] closed a-little [poss-の] while couch [on-に] lie-down [imperative-なさい].
長椅子 ('long chair') is the native Japanese term for a couch or chaise longue. 横になる ('become horizontal') means 'lie down.' The te-form chains 閉じて with the main command. 少しの間 ('a little while') uses の to connect the adjective to the noun.