You may already be aware of this, but there are records at the FamilySearch database [https://www.familysearch.org] for John and Jane, as well as three of the children you mentioned: Charles, Elizabeth, and Jane. If you create a (free) account at the site, you can find John at ID #LCZJ-K1C, and can access the records for the others easily from his record, as you will see.
Unfortunately, the creator of those records does not appear to have more specific info about their birthplaces in Ireland. Her screen name appears to the right on each record which she created or modified, though, and you can send a private message to her through the site, so you could compare notes (if you don't already know one another).
Irish surnames (particularly those of Gaelic origin) are often peculiar to a specific region or county (sometimes even a part of a county), and that can help with genealogical research. The surname McGuigan (in Irish Mac Uiginn) originated in County Tyrone, in what is now Northern Ireland, and is still found mostly there and across the border in County Monaghan, so that may help narrow down your search. It has also been anglicized in a number of other ways, such as MacGoogan, MacGookin, MacGuckian, MacQuiggan, MacWiggin, Wigan, and Maguigan, and in County Monahan as Pidgeon or Fidgeon. Different anglicized forms were sometimes used within the same family, so don't be put off if you find potentially relevant records with any of the variations. One of the documents attached to the records at FamilySearch also shows the name as McGurgan.
I noticed at the NLI church records site that there is a Catholic parish in Tyrone called Termonmacguirk. I have no idea whether that name is somehow related to your surname, but it's not far from the border with Monaghan and the parish records go back pretty far, so if you want to do some searching around there, you can find the records at this link:
https://registers.nli.ie/parishes/0196 (at that site, there's an interactive map which allows you to move on to neghboring parishes as well)
There is also a civil parish of the same name, with what look to be the same boundaries (which is not always the case), and you can find more info about it at this site:
https://www.townlands.ie/tyrone/termonmaguirk/
At that site, there's a list of all the townlands in the parish, with links to more info about them, so if you manage to find a baptismal record which indicates the townland where the child was born, that list might be useful (it has maps of the townlands, and links to other records as well).