I was able to make out the name and date of the two and confirmed their marriage was January 1, 1862. However, I can not make out the other writing, nor does it give any indication of age or parents. Any other tips?
The townland in the last column looks like a shorthand version of the one on the civil record of the birth you linked to on wikitree, namely Drummullagh.
To figure out their parents you are going to have to work backward. Are they on the 1901/1911 censuses? when did they die? how old did it say they were when they died? Rose had children for 19 years, that is a clue to when she was born. Not so much for her husband.
Do their children's names provide a clue? For example, was one of their mothers Elizabeth and the other Margaret? They only had two sons and neither were named Michael. Were they named after their grandfathers?
How many Quinn families were in that townland? Where were the Connollys, same townland or not? Can you find siblings that were married a few years later, so their record would include the father's name and both townlands?
Where did their children go and do their records tell you anything?
I don't think it is going to be easy to narrow down which Quinn and Connolly is the right family.
