Deb,
I see a marriage for an Andrew Johnston to Anne Johnston (ie maiden name Johnston) on 20.2.1861 in Enniskillen. Have you looked at that to see who the father was and what addresses the couple were living at? You can view the original certificate on-line on the GRONI website, using the “search registrations” option:
https://geni.nidirect.gov.uk
You will need to open an account and buy some credits. It costs £2.50 (sterling) to a view a certificate.
Tradition was to marry in the bride’s church which should be on the certificate (unless it was a Registry Office marriage). That church may be the place to look for her baptism and that of any siblings.
Statutory birth registration only started in Ireland in 1864, so you won’t find a birth certificate for Andrew or any of his siblings.. Prior to that you need to rely on church baptism records, where they exist. You don’t say what denomination the family was. If Church of Ireland (ie Episcopalian) then the Enniskillen baptism records for the period you are interested in are lost (destroyed in the 1921 fire in Dublin). There are some for the Church of Ireland at Tempo which start in 1836 (copy in PRONI). If Methodist then Tempo has baptisms from, 1841 onwards (copy in PRONI). Presbyterian, then the Enniskillen Presbyterian church has records as follows: Baptisms, 1819-35 and 1837-1986; marriages, 1819-34 and 1838-45; If RC, then baptisms start in 1838, marriages in 1817. They are on-line on the nli site.