Hi Nutkin
I'm guessing you have found out more about Michael Cochrane by now as your post is some years ago, but will tell what I know.
He is in the 1841 Census - Loudoun, Darvel parish
aged 65 Hand loom weaver, not born in same county
wife Isobel aged 55 not born in same county.
A Michael Cochran married Isobel jamieson 13 Nov 1829.
Michael Cochran married Agnes Mair 1795 at Loudoun (not found exact date yet).
I'm surmising Agnes died and Michael married again.
The children of Michael and Agnes are Agnes 1 Feb 1798
Michael 1 Feb 1798 (twins or just waited for the next one to christen the first?)
James 14 Jan 1800
Mary 18 April 1802
I think there may be a couple more but not found them yet (see below).
Michael Cochran snr that you are looking for died 3 Oct 1850 at Loudoun, Darvel parish aged 74. I have a little leather notebook written by Michael Cochran jnr starting about 1850 until his death in about 1871. It is a list mainly of people's deaths, and other little interesting snippets! Some of the names I have yet to match up to people I have found, but one entry is the death of 'Michael Cochran my father diead.......'. I can scan in the page and send it you if you'd like.
So on Searchlabs family search there is a birth of Michael Cochran 11 March 1775 at Srathaven Lanarkshire of Alexander Cochran and Mary Smith, which looks likely but will need some confirmation. Not sure how to go about that this far back! For another day!
Michael Cochran snr was my gggggrandfather through his son Michael.
Any other info you have found I'd be interested to see.