I search the IFHF's online database @ ROOTSIRELAND.IE. It has abt 19 million B/M/D and other records for MOST Irish counties. Records before 1863 are increasingly sparse and al most non-existant prior to 1800. Many early B/M/D events weren't recorded, or the records didn't survive.
For Chris(topher) Kelly B 1847 (exact), Co. Kildare, with a father forenamed W(illiam), I found 1 record. The mother's forename is BRI(GID). A view of the detailed B record SHOULD show the parents' complete names. The mother's name, if found, should help you with the below.
For W(illiam) Kelly M 1844 +/- 3 yrs, Co. Kildare, with the parents names unknown, I found 1 records. The bride's name is Bri(DGET).
For William Kelly B 1820 +/- 4 yrs, Co. Kildare, with the parents' names unknown, I found 13 records.
Hope this gives you some useful clues. Good luck and merry Xmas.