Hi Kathleeen, the site here is https://www.irishgenealogy.ie/en/ Under the civil button on top of page and sign in, free to do so and any records you want in the period should be viewable on the full page, I snipped out the pieces I attached. It also has the Dublin and Cork church records but not a lot more for the churchs.
I would imagine there was a church there of sorts, a friend of mine owns a house outside Cobh overlooking the harbour and Spike Island, I am always jealous when I visit. However I am not the local volunteer, I live about 200 miles away and was picking up questions that were missed or overlooked over the Christmas, also we may not have a volunteer in the area as it was posted under Dublin so the Cork volunteer may not have looked at it, I like unusual names like Scart. There are so few it may be only one family, the Hanlon name is the one attached to the Chieftains or O'Hanlon, the O was a movable feast, with the upsurge in nationalism post famine people people added in the O, there are many theories around it but I even notice it in my own family, one generation in the next out etc.
If you can email here they should be able to tell you about the church https://www.cobhheritage.com/ He first marriage to a Hosford could probably be found and give her home parish and address, there are Hosfords in Cork.
Without realising it was you I had looked at Corbett but nothing jumped out, could find not births in Cobh and Imprick is a good distance away near the Limerick county line. Is it possible the embarked from Cobh as it was the major emigration port and people travelled from all over Ireland to there, ah la the Titanic.
I will revisit this in the next few nights but it is almost 1 am and time to nod off. I will send or attach the info on O'Hanlon from McLysaghtss book of surnames at some point.
https://www.johngrenham.com/findasurname.php?surname=O%20hanlon just a little here, a sept is the Irish Gaelic version of a clan in Scotland but has been overtaken by the word clan.
Regards
Pat