Cheryl:
Welcome to Ireland Reaching Out!
Ballybricken is an RC parish but not a civil parish. The Tithe listings are filed by civil parish and I believe the Timothy Dwyer you are looking for was in Ludden civil parish. This record is from 1826 and if this is your ancestor, he was leasing about 13 acres of land. http://titheapplotmentbooks.nationalarchives.ie/reels/tab//004625695/004625695_00270.pdf
However, in the 1850 Griffiths Valuation head of household listing for Ludden civil parish, no Dwyer is listed https://www.failteromhat.com/griffiths/limerick/ludden.htm which implies that Timothy was deceased or moved to another location. When Margaret Dwyer married in 1864, the parish was St. John's in Limerick city so did your Timothy lose his holding and move to Limerick city?
I searched on the subscription site Roots Ireland and they have Ballybricken baptismal records back to 1800, however, I did not locate any baptismal records for children of Timothy Dwyer and Mary Dillon anywhere in Co. Limerick. Since you have the baptismal records, can you tell me the parish where the baptisms occurred?
Roger McDonnell