Hello Sue,
Civil registration only began in Ireland in 1864, any records before that are church records. Most church records start approx 1820 or so , but some old towns may have records going back to 1790 ish.
You will find many church records between two online sites www.irishgenealogy.ie which deals with about 5 counties in Ireland. This site is free. The other site which would deal with Co. Leitrim is www.rootsireland.ie This is free to join and search but you would have to pay to open and view/print a particular record. This site is offering 40% off until October 13th so you may have started your search at an opportune time. The price to view a record is usually about €5 but will be cheaper for a few weeks.
The name Ingoldsby is found on both sites and is surprisingly plentiful here. I would advise that you keep a very open mind in your search regarding dates and places.
Most people who emigrated were illiterate and undocumented. They didn't know how to spell their names and hadn't a clue as to what age they were. At the port of arrival their names were recorded phonetically, their ages were only guessed, and this is the information that followed them for the rest of their lives.
The proof of this occured in 1909 when the old age pension was introduced into ireland. People had to prove their ages and were forced to go through baptismal records to establish when they were born. That is why there is such HUGE discrepancies between ages in the 1901 census and the 1911 census of Ireland. Dates were found to be out by many many years in some cases.
I hope this helps you on your way,
Anne Dennehy