I'm interested in St. Monans families myself, so I've been poking around on Scotlandspeople. Usually you can solve all your BM&D queries online, but there are complications in this case.
I found a James Allan INNES, born in St. Monans in 1917, but it's a "no image available", meaning that his birth-certificate has not yet been digitised. You would have to go to Register House in Edinburgh to look at it.
He is no doubt the James Allan INNES who married Catherine ALLAN (a cousin?) at Dundee in 1940, but again it's "no image available", so I can't check who their parents were.
A James INNES and Elizabeth ALLAN were married in St. Monans in 1900, but I can't prove that they were your ancestors.
Both these surnames have been common in St. Monans for a long time. My secondary school in Anstruther (Waid Academy) drew its pupils from all the villages in the East Neuk of Fife, and I knew lots of kids from St. Monans. In my class there was an Evelyn INNES and a Gilbert ALLAN, both from St. Monans, and Gilbert's father had been in my dad's class in the 1920s. The school secretary was a Jean ALLAN from St. Monans.
I have some distant family connections with St. Monans ALLANS.
Harry