Hi Gary,
I have a directory of Belfast and the Province of Ulster Volume 1 - 1852. Anthony mentioned Israel as his name appeared in this directory. There were several others - 10 in fact. It may be worth while making a note of them. I see you have not commented about your great grandfather's parents so the names below may prove useful at some stage in the course of your research.
Directory of Belfast and the Province of Ulster 1852
Emanuel Milliken, master mariner, 7, McCrory's Row, Ballymacarrett
Elizabeth Milliken, 48, Little Patrick Street
George Milliken, publican, Falls Road
James Milliken, hatter, 65, Green Street
Jane Milliken, lodging house, 4, Gordon Street
James Milliken, boot and shoe maker, 44, Cromac Street
Margaret Milliken, dressmaker, 64, Donegall Street
Robert Milliken, grocer, Falls Road
Robert Milliken, saddler, 49, North Street and 21, Long Lane
William Milliken, ostler, 11, Little Donegall Street
There was a Robert Millikin, publican, at Whiteabbey. I suppose typesetting errors occurred occasionally. I mention Robert as he is on the Islandmagee side of Belfast.
It may be worthwhile having a closer look at Emanuel Milliken. Many mariners came from Islandmagee. He may have moved from that part of Co. Antrim to Ballymacarrett to be closer to the docks in Belfast.
Best Wishes with your research,
Christopher