Not sure if you have already tried this site in Halifax. It is a Parks Canada info site about the Military Museum in Hfx.located at the Halifax Citadel. Info.from 1749 - WW2. http://www.pc.gc.ca/lhn-nhs/ns/halifax/visit/visit11.aspx
Also I have found some info about the regiments in the book by John Kitzmiller 11 - 1988, entitled "In Search of the Forlorn Hope" - A Comprehensive Guide to Locating British Regiments and their Records, vol.1 and 2. Don't believe they have much on births though. I found a great great Aunt born in Fredericton NB after contacting the archives there and had the good luck to find an archivist who searched the info for me at no cost! Good Luck!