I didn't know that. Buchanan has a poem in praise of Elizabeth, addressed to the god Janus in January 1568 asking rhetorically "what can you ask for for somebody who has everything?" - it's very cleverly constructed. But the metre doesn't fit any kind of Scottish tune I can think of:

Jane pater, solus partes qui versus in omnes
Quicquid habet tellus ante retroque vides:
Prospice quae possim non dedignanda Kalendis
Saxonidum dominae mittere dona tuis...

BTW by that point Buchanan was sufficiently pissed off with Mary (his employer) that he was dropping broad hints that political assassination might not be unthinkable.