Hi Jane...me again....
Did an even better look see around the IGI and came up with a few more records that appear to all belong to Francis and Mary...
FRANCES SHIELDS - International Genealogical Index
Gender: Male Birth: 19 MAY 1866 , , Ireland
MARY JANE SHIELS - International Genealogical Index
Gender: Female Birth: 22 DEC 1871 , Tyrone, Ireland
Annie Sheals - International Genealogical Index
Gender: Female Birth: 24 FEB 1877 , Tyrone, Ireland
Eliza Sheils - International Genealogical Index
Gender: Female Birth: 14 MAR 1879 Omagh, Tyrone, Ireland
Of special note is the birth of a Frances in 1866. This pretty much confirms the fact that they married in Scotland but left for Ireland before too long. Still no sign of John.....
oh wait...found more from the BIVRI disks...
SHEALS, Catherine Birth
Gender: Female
Birth Date: 3 Mar 1868 Birthplace: 281, No 1 Belfast, Ant, Ire
Recorded in: Antrim, Ireland
Collection: Civil Registration
Father: Francis SHEALS
Mother: Mary LAPPIN
Source: FHL Film 101160 Dates: 1868 - 1869
and further details on the Frances on the IGI given above...
SHIELDS, Frances Birth
Gender: Male
Birth Date: 19 May 1866 Birthplace: 311, No 1 Belfast, Ant, Ire
Recorded in: Antrim, Ireland
Collection: Civil Registration
Father: Francis SHIELDS
Mother: Mary LAPPIN
Source: FHL Film 101125 Dates: 1866 - 1868
and further details on the Mary Jane listed from the IGI above...
SHIELS, Mary Jane Birth
Gender: Female
Birth Date: 22 Dec 1871 Birthplace: 336, Omagh No1, Tyr, Ire
Recorded in: Tyrone, Ireland
Collection: Civil Registration
Father: Fancis SHIELS
Mother: Mary LAPPIN
Source: FHL Film 255841 Dates: 1871 - 1872
Sadly there does not seem to be anything yet on your John.
Now changing gears I've been off looking for Mary's family. Doesn't help that she states her mother's maiden name as Busby on the 1864 marriage, Lappin on the 1907 marriage, and it's stated as Graham at Mary's death. And not one of them pops up in the IGI with a birth of Mary or a death........but she's there on the 1861 census with Mary and a whole slew of others in the household.....this is how Mary is indexed on that one.
1861 MCCONN MARY F 15 CLYDE GLASGOW CITY/LANARK 644/05 021/05 013
Oh yes....another important lesson here. Mary's dad is listed as Peter but you'll see he's enumerated as Patrick. Gotta still use them wildcards all the time with this bunch!
You'll find her hubbie to be Francis not far away with his whole family too.
1861 SHIELD FRANCIS M 15 CLYDE GLASGOW CITY/LANARK 644/05 027/05 005
Ok....it's past my bedtime

.......I think you can take it from here.....
Best wishes
Jean