Oh boy, just lost my post to the ethernet. Will try again.
Michael C Boyce, Cooper, and the Army....
It looks like the Michael C Boyce who enlisted in 1855 was discharged in 1857 because he was a minor, so he must have lied about his age to join up. This same man then enlisted again in 1858, this time at Boston if I remember correctly. Both times he gave his birthplace as St John New Brunswick which would be a fair way from Nelson Parish in northern NB. So it doesn't appear that this Michael is the same man as Minnesota Michael.
In the 1905 Minnesota census Michael indicates that he has been in the enumeration district for the preceding 50 years which would place him there since about 1855.
Baptisms of the siblings....
-Bridget Boyce b. 09 Oct 1826 bapt. 28 Jan 1827. Of lawful marriage of Patrick Boyce and Catharine Hallaran
-Eliza (as written) Boyce bapt. 17 May 1829 age 2 months. Parents Patrick Boyce and Catharine OHallaran
-Catharine Boyce bapt. 18 Jun 1831 age 4 weeks. Parents Patrick Boyce and Catharine Holaran
-Michael Boyce bapt. 28 Aug 1833 age 2 weeks. This is quite close to the birth date posted by JimPeterson and the familysearch transcript has a birthdate of 04 Aug, also close. It is really too bad that the death record didn't name the parents. Perhaps a marrige record might if you choose to go that route.
I didn't see a baptism for Ann but we do have her with Michael and Bridget in the 1852 census. Bridget married James Moran in 1847.
A variety of last names for the mother for sure. Parish records from that time tend to have names spelled as they are heard by the priest. And different priests may hear things differently. At least Boyce is consistent.
The question now is whether these parents belong to Minnesota Michael. Tough call. We don't know if all NB records are on line and so there could be another family somewhere. On the other hand, the closeness of the various quoted birthdates is quite compelling.
What would I do if I were in your shoes? I would try to get a marriage cert when circumstances permitted. You have an approximate time frame with the birth of their first child Joseph. No guarantees that your money will find what you want, of course, but would be money well spent if you get a record with parents.
PB