Couter to rhyme with scooter was the country pronunciation.
It is only in recent years that I came across Ewan MacColl in The Tobar an Dualchais site, before that if I had heard his name it did not register. I asssume that the recordings on that site were made in his early days while he was still working up to a Scots accent for to be quite frank, to a native speaker, his Scots accent in those recordings sounds so artificial.
As those were the only recordings of him that I have heard I cannot comment on how he developed it in later recordings.