From the records I have, there was a William Colter listed on the 1860 US Cenus with children by the name of Samuel, James, and Miller (all 3 names appear in my lineage as brothers). That would mean that William came from Ireland. There is an Archibald Coulter listed in the "Griffith's Valuation of Ireland 1848-1864". I have not checked further into it, but this may be the Archibald you are looking for. William has children with dates of birth prior to 1829, so I don't think they are related. I will keep checking and keep you posted on what I find.

Thanks,
Leigh