I've just inherited family papers and photos relating to my great-grandfather, James HW Hay of the Seaforth Highlanders. There is a letter from Buckingham Palace granting permission to wear 'the Gold Medal of the Order of "La Maison Ernestine" presented to you by The Duke of Saxe Coburg & Gotha'. This is November 1910 when the Duke was Colonel-in-Chief of the Seaforth Highlanders, so fits with your information above.
There's also a newspaper clipping (no date) from when he re-joined the regiment at the start of WWI which refers to his 4 medals 'one of which he will no longer wear, although it will be kept in the family as a curio. It is a gold medal presented to him (for meritorious service) by the honorary colonel of the regiment... a German prince, the Duke of Saxe-Coburg Gotha'.
Sadly, I've no idea where his medals ended up, so only have a paper trail!