1. One of the two transcriptions I can see of the church record of marriage in St. Patrick's Belfast in 1884 cites
both parents for bride and groom, namely Bernard and
Mary Moane from Co. Fermanagh and Peter and Jeanette Dugan.
2. A clearly identifiable military record for Michael exists (military ref. no. 1761) in that it mentions his wife (albeit recorded as 'Mary' Dugan) and a date and place of marriage of '13 April '84' at 'St Patrick Belfast'. In an attestation on 14 May 1878, Michael was described as having been born in the parish of Clogher, near Fivemiletown in County Tyrone, his age was 18 years 0 months, he was a tailor by trade. Before this attestation to the regular army (64th Brigade), he had been conditionally released from the Royal Tyrone Fusiliers. Moving forward to May 1884 (shortly after marriage), he was transferred to the Army Reserve. There is a further 1890 attestation under the Army Reserve to the 2nd Bn Royal Inniskilling Fusiliers and he was then discharged in April 1894.
The only reference in these documents to next of kin are the words 'Bernard Father Brookeboro Fermanagh'.3. In the circumstances, it is worth simply noting for now that a couple called Bernard Moane and Mary Nann/Naun/Vaun are on civil record as having a number of children in the 1860s through to the 1870s, the address was Eshnasillog in the parish of Aghalurcher, it's just possible that these were younger siblings to Michael who was born pre civil registration, here was that Bernard's widow and children in the 1901 and 1911 censuses (Bernard having died in 1893):
http://www.census.nationalarchives.ie/pages/1901/Fermanagh/Grogey/Esnasillog_Beg/1356718/http://www.census.nationalarchives.ie/pages/1911/Fermanagh/Grogey/Eshnasillog_Beg/522681/There again, there is nothing else to tie these folk down more conclusively as being Michael's family, the surname is not uncommon for the area (nor is the forename Bernard), so treat as speculation until they can be ruled in or out. You can find various records for these folk on the 'IrishGenealogy' website.