The advice by Beatrix is very good (assuming your ancestor was Roman-catholic). The Diocesan Archive has an index of all births from around 1900 or later. 1888 maybe within reach there. This index is only accessible by archive staff.
Does the marriage certificate really not have any indication of the birth parish? Could you scan and send me a copy of the certificate? There are also other means to find out more about your ancestor, such as the residency records, or the records of the 1880 census.