Dont see Teresa's birth registered in Dublin so is she one of the Female births in Dublin North.
The reason i say this is you say you have 3 birth certs do they not give James's occupation.
and to note with her baptism being St Andrew's perhaps they married there between 1900 and 1902.
Which leads to church microfilm for St Andrews
http://www.nli.ie/en/parish-register.aspxclick on Parish Register List Cork and Dublin opens in PDF
Alphabetical list scroll down to S for St Andrews ,cut off date for marriages July 1st 1900 and its possible James and Annie got married between this date and 1902.
I have got a marriage cert from the front office at St Andrews a couple of years ago but i will admit it was for 1894 but still leaves the possibility that you could ask for a search if they still have the registers in house after 1900 they charge a fee no idea how much.