Which preposition to use with couchant

at Occurrences 1%

Crusoe mounted guard by stretching himself out couchant at Dick Varley's side.

on Occurrences 1%

Then, if you please, imagine her asking for his card, whereupon he exposes the side of his new tin shield, on which is painted in large Old English letters a Latin motto meaning, "It is the early bird that catches the worm," with bird rampant, worm couchant on a field uncultivated.

Which preposition to use with  couchant