I wonder if there was any connection between James Rodgers, bottler, in the 1877 directory at Murphy Street, and your Isaac Rodgers.
1870 Page 346
Murphy Street
11 Wheeler & Co Aerated Water Manufacturers
1877 Pages 222 - 223 (also on Mary Lennon's website)
Murphy Street Page 222
Numbers: 3-19 Wheler & co Cromas Springs, Manufacturers of aerated & mineral water (celebrated Belfast gingerale), general bottlers, and manufacturers of British Wines.
Number: 21 Rodgers, James, bottler
From Mary Lennon's website: 1880 - Numbers 3-25 Wheeler & Co, Cromac Springs, Manufacturers of Aerated & Mineral Water.
PRONI - Belfast /Ulster - Street Directories online:
http://www.proni.gov.uk/index/search_the_archives/street_directories.htmList of directories scanned
•Bradshaw's General and Commercial Directory for 1819
•Belfast Directory 1831-32
•Matier's Belfast Directory 1835-36
•Martin's Belfast Directory 1839
•Martin's Belfast Directory 1841-42
•New Directory of the City of Londonderry and Coleraine, including Strabane with Lifford, Newtownlimavady, Portstewart and Portrush
•The New Commercial Directory of Armagh, Newry, Londonderry, Drogheda, Dundalk, Monaghan, Omagh, Strabane, Dungannon, Lisburn, Lurgan, Portadown and neighbouring towns
•Martin's Belfast Directory 1842-43
•Henderson's New Belfast and Northern Repository 1843-44
•Henderson's Belfast Directory and Northern Repository 1846-47
•Henderson's Belfast Directory and Northern Repository 1850
•The Belfast and Province of Ulster Directory 1852
•Henderson's Belfast Directory and Northern Repository 1852
•The Belfast and Province of Ulster Directory 1858-59 Volume 4
•The Belfast and Province of Ulster Directory 1863-64 Volume 6
•The Belfast and Province of Ulster Directory 1865
•The Belfast and Province of Ulster Directory 1866
•The Belfast and Province of Ulster Directory 1870
•The Belfast and Province of Ulster Directory 1877
•The Belfast and Province of Ulster Directory 1880
•The Belfast and Province of Ulster Directory 1884
•The Belfast and Province of Ulster Directory 1887
•The Belfast and Province of Ulster Directory 1890 Volume 13
•The Belfast and Province of Ulster Directory 1892
•The Belfast and Province of Ulster Directory 1895 Volume 16
•The Belfast and Province of Ulster Directory 1896
•The Belfast and Province of Ulster Directory 1897
•The Belfast and Province of Ulster Directory 1899 Volume 20
•The Belfast and Province of Ulster Directory 1900