If the age of Dennis on his father's death certificate was correct, and, if he was, like his father, born in County Clare, and if the family was R.C. this baptism is very likely his.
Catholic Registers at National Library of Ireland.
Doonass & Truagh Parish, Diocese of Killaloe, County Clare
1852 August 29th Dennis Davis, parents John Davis & Judy Hogan. Their residence begins with C (I
think). Sponsors (godparents) John & Jane Murphy. Another column also has heading "Residence" (I
think). It may be for residence/s of sponsors. The place looks like Clontara.
https://registers.nli.ie/registers/vtls000634681#page/7/mode/1up
Residence of the sponsors was probably Clonlara, a village and R.C. parish.
Parish of Clonlara (Doonas and Truagh), Diocese of Killaloe
https://www.killaloediocese.ie/parish/clonlara-doonas-and-truagh/Doonas & Truagh R.C. parish covers the civil parish of Kiltenanlea + lowers parts of O'Briensbridge civil parish + townlands in southern part of Kilselly civil parish.
A website for Clare County Libraries with comments about the Catholic registers.
www.ourlibrary.ca/phpbb2/viewtopic.php?t=5840&view=previous Civil parishes in Ireland were administrative areas. Each civil parish contained several townlands. A townland is the smallest land division in Ireland, although some townlands contained sub-townlands. A civil parish may also contain a town or towns and/or a village or villages.
Griffith Valuation was a survey of land holdings in mid-19th century Ireland. The survey and compilation of findings took years to complete. Database can be searched by a person's name.
https://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch3 results for John Davis in County Clare.
1 John Davis was in Coollisteige townland in Kiltenanlea civil parish. He rented a house and 2 acres of land. He may have been the John Davis who went to Australia, or his father, or another relative, or no relation.
Patrick Hogan occupied property in Coollisteige townland. (Wife of John Davis & mother of Denis Davis was Judy/Joanna Hogan.) There were other Hogan holdings in Kiltenanlea parish.
Cloonlara Village and Cloonlara townland are in Kiltenanlea civil parish. 3 holdings in Cloonlara Village were held by 1 or more men named John Murphy. (Godfather of Denis Davis was a John Murphy of Clonlara.)
Kilseily civil parish. A Richard and Geo. Davis + 2 other men were immediate lessors (landlords or "middlemen" letting or sub-letting property and collecting rents from occupiers).
OBriensbridge civil parish. There were Davis occupiers and Davis immediate lessors.