You probaly know the Ballyvaughan baptismal records start in September 1854 https://registers.nli.ie/parishes/0613 so if Thomas Burns and/or Margaret Howard were baptized in that parish, a record would not exist. On the subscription site Roots Ireland, I did find a Margaret Howard baptismal record in Tubber parish which is a few RC parishes to the east of Ballyvaughan. This Margaret was baptized January 1 1836 parents Patrick Howard and Mary Howard. I did not find amy possible records for Thomas Burns on Roots Ireland.
I also looked for a Patrick Murphy baptismal record in both Co. Clare and Co. Tipperary but did not find a record.