I checked the Family Search database [https://www.familysearch.org], and there have been two sets of records created for what appears to be your McGowan family, with two separate records for Patrick (which need to be merged, but I'll leave that to you or other family members). You can find the two records for Patrick under these ID numbers, once at the site (once you set up a free account):
ID # L6FD-RTN, showing a son named James McGowan, born 24 Dec 1874
ID # 894CM-LX6, showing a daughter name Honora Jane McGowan: 9 May 1886
One set of records shows the mother as Honoria Frain, and the other as Honor Frain, but the various forms of the given name Honora were often used interchangeably in records.
In each record at Family Search, at the right hand side of the record you can see the screen names of those who have created or modified the record, and can send them private messages, so you might be able to get more info by contacting them (and perhaps also locate some relatives that way). If you merge the records for Patrick and Honora, and add the names of the other known children, the Family Search software will start looking for documents relevant to the family, and should eventually find the civil birth records for all of the children, possibly turning up the child you have as "P" and whoever came later. Modifying records can take some practice, but the database is really good (it's the largest in the world), so in the end it could be very worthwhile. It's run by the LDS church, so they have classes in using it at their Family History Centers (there is at least one in the Vancouver area). Everyone is welcome there, and no one will bother you about convertnig or anything like that (I'm not a Mormon and I've used their centers many times).
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