For David Larmin B 1861-1865, Co. Kildare, with a father forenamed James, I found 1 rcd, Caragh RC parish.
For James Larmin M ????, Co. Kildare, I found 0 rcds.
Note - the Kildare portion of the database doesn't contain civil B/M/D rcds. Contact the General Register Office at http://www.groireland.iehttp://www.groireland.ie to see if these rcds survived the Four Courts fire of 1922.
For Eliza Stafford B ????, there are 0 M rcds at any date, and several B rcds, none of which fit your timeline.