If you have checked the records for Bansha then there is almost no way you will be able to find to access birth records.
I would look for gravestone inscriptions. There is a gravestone index on www.from-ireland.ie
but not sure what you might find there. Often local museum and heritage groups
collect inscriptions and put them in journal form. There is also a UK firm who charge for their records collected in 1888 and Bansha is one of the graveyards listed.
As this is a commercial entity you will need to contact me, as rootsweb/ancestry do not allow the websites of anything that is not FREE it is a membership firm but you can get a short membership and they do have a monthly membership but it is expensive.
I would try other alternative first and then if desparate for information try that.
There are Church of Ireland marriages from Bansha available from 1845-1864. I could look these up for you as I have them on CD.
In 1852 Griffith Valuation took place in
Tipperary, a tax on land:www.failteromhat.com
look for matching Parish's of the names you mention then proceed to a more detailed valuationwww.askaboutireland.ie
Tithe Applotments 1820-1839 tax on land:www.genealogy.nationalarchives.ie
only gives Townland and Parish.