Have you checked the NAS catalogue? The NAS holds many family papers that can include charters, bonds, etc.
Some entries for King of Dryden:
Instrument of Resignation by Mr Alexander Kinge [King] of Drydane [Dryden], advocate, of 10 acres of lands of Pentland, in favour of Mr John Nicolsone [Nicholson] of Leswaid [Lasswade], commissary of Edinburgh, and Elizabeth Henrysone [Henderson], his spouse. 8 Jun 1601
Charter de me by James King of Drydane, advocate, with consent of Janet Dowglas, his spouse, to Mr. Robert Bruce, son to deceased Sir George Bruce of Carnock, knight, of annualrent of 800 merks Scots furth of lands of Nather Inzievar 14 Aug 1628
There are also some documents mentioning King and Burnhouse.
Stefan Ramonat