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I noted this birthplace from the FindmyPast transcription.  You could try the original image at Scotlandspeople, although I would doubt there would be anything else.  Consider it a bonus to get more than Ireland as place of birth !

However, on a more general point, then James' parents, James Fulton and Unknown McNeill could very likely be the James and Ross (Rose) Fulton also living in Ewing Street in 1841 and were related to the Hugh Fulton and Mary McNeill, also living in Ewing Street, ie they could be brothers Fulton marrying sisters McNeill, and migrating to Renfrewshire about 1815/1820.   

Hugh Fulton and Mary McNeill were both born Ireland, probably about 1790 and 1800 respectively - they had six boys all born in Renfrewshire. Hugh and Mary were both deceased before 1858, and I suspect, before 1851.

However, in the absence of any other information to go on, then a search for this family in Co Antrim could turn something up.  I have no experience of searching for Irish records around the early 1800's but I have heard it can be difficult. Good luck.

Regards
Stuart

Just a brief follow-up - the OPR marriage record between John Robertson and Margaret Tower in Aberdeen is as follows:

Upon the Twenty Eighth day of July, On Thousand Seven Hundred and Ninety Five by the Revd Mr James Ross one of the Ministers of Aberdeen were lawfully married in the House of the Bride's Father in Aberdeen after Due Proclamation of Banns. Mr John Robertson Mercht in Berwick and Miss Margt Tower Daughter of John Tower Cooper there in presence of these Witnesses Robert Tower Mercht in Aberdeen and the said John Tower.

This would suggest that the Tower family originated from Aberdeen with at least one merchant and one cooper.

Stuart (Aberdeen)