My top suggestions for baptism of John Tierney are St. Wilfred's and St. Augustine's. They are equidistant from Syke St. Registers for both churches are at Lancashire Archives.
St. Augustine of Canterbury, St. Austin's Place, (not far from Avenham Lane), founded 1838. It had a cemetery.
Registers at Lancashire Archives: Baptisms 1840-1922; marriages 1841-1902; burials 1855-1914.
St. Wilfred, Chapel St., founded 1792. It had a cemetery, closed 1854.
Registers at Lancashire Archives:
Baptisms 1768-1803; 1813-1898;
Marriages 1769-1803; 1813-1829; 1856-1899
Burials 1768-1803; 1817-1854*
St. Wilfred was successor to St. Mary which was known to have existed since 1605, hence registers pre-dating foundation of St. Wilfred's. St. Mary closed when St. Wilfred opened but re-opened a few years later to cope with the increased congregation.
Information from Lancashire Online Parish Clerks and GEN UKI websites. This information may not be up to date. GEN UKI is a vital guide for FH research. Among other things it lists churches in a town. Just google GEN UKI and a place. Both sites are volunteer- run.
* The former St. Wilfred cemetery has a website. It was too early for your Tierney family though.
There were 7 Catholic churches in Preston (including St. Mary) when Bridget & John's children were born there, so not knowing addresses when the older ones were born it would be necessary to look up baptism registers of all of them. I'd begin with St. Wilfred and St. Augustine in case the family remained in same area.
As for burials, possiblities include St. Augustine, St. Joseph, (burial register from 1877 at Lancs. Archives), St. Ignatius (burials registers 1836-1855 & 1880-1916 + monumental inscriptions 1832-1858 at Lancs. Archives) and Preston cemetery. Catholics were also buried in C. of E. churchyards if there was no cemetery or R.C. graveyard. Don't expect to find tombstones, the family wouldn't have been able to afford them.
Lancashire Archives has indexes to some registers. LANCAT is the online catalogue.