Do you want songs specifically where the hawk is the central theme or are mentions enough? There are plenty of songs where they get a mention or are being included allegorically. The Pretty Grey Hawk is of the latter type as it is really a lover being described. Plenty of Lords in ballads have their hawks mentioned. Then there's 'Jolly Old Hawk' a carol similar to the Twelve Days of Christmas.

There is also a commonplace in many songs that mentions having the wings of an eagle and flying to a truelove who is far away, but other birds are also used in this.

Otherwise Googling ought to turn something up if there is anything.