Does your grandmother have other living relatives (brothers, sisters, children) that you could ask for more information.
If you have her death date and place, get a death certificate, if may list her birth date, although it will probably just say b. Ireland.
If she emigrated from Ireland to somewhere else, she may be on a ships manifest. Did she become a naturalized citizen, applications have a wealth of information. If she emigrated with her husband or parents, their applications may have information about her.