What sort of notices are you looking for? In general, birth notices are quite rare and usually only gentry or tradespeople put such in the paper. Marriages a bit more common and deaths occupy the most space in the announcements. The social status and literacy of a family can determine in they would have paid for an announcement. It also depends on the individual family- I checked for notices for several well-to-do ones and found nothing but I do know that they had death letters printed and delivered to relatives, neighbours and friends so likely thought nothing else was needed.
I've not seen the Derry Journal online anywhere.
Added- if you are able to find a newspaper notice the details will be minimal. Here are 3 examples:
Birth Londonderry Sentinel, 25 Dec.1857: At Tullyhoe, Newtownlimavady, on the 19th inst., the wife of Mr. William Brown, of a daughter.
Marriage Londonderry Sentinel, 1862: On Thursday, the 6th inst., in Great James Street Presbyterian Church, by the Rev. Robert Ross, Mr. John Clements, to Maggie, second daughter of the late Mr. Samuel Milligan, of this City, printer.
Death Londonderry Sentinel, 1861: At Ballykelly, on Friday, the 24th inst., Margaret, wife of Mr. Thomas Clements, aged 75 years.