Baptism record in the Parish register, RCBL, #P429.011.
It is a bit challenging trying to sort out the Williams. The baptism register for children of William and Eliza Clarke indicates that William Clarke, Esquire was of Rathleague. Rathleague is the townland immediately east of Meelick, home of the Thomas Clarke family. The 1850 Griffiths Valuation shows Wm. Clarke occupying a house in Rathleague, as well as two different William Clarkes holding land in the townland of Borris little (Borris civil parish) where there are records of land holdings for both a "Wm. Clarke, jun., Esq." and "Wm. Clarke, sen., Esq." Wm. jun. occupies a house in Borris, little. Wm. sen. holds land, but does not occupy a house there. My guess is that Wm. of Rathleague could have been Wm. sen. of Borris.
There is also William Clarke in the Griffiths holding Block 3 A, B, C & D in Killimy, leased from the Earl of Portarlington: a total of about 20 acres; valued at £9/10. A house on Block 3D was subleased to Michael Salmon. As well, a William Clarke, whose wife was named Catherine leased land in Morett--one of the three Morett holdings included a house, so that is probably where he lived--altogether, we are still trying to sort out the Williams.
Death notice in "Freeman's Journal and Daily Commercial Advertiser," 13 June 1882: "CLARKE -- June 11, 1882, at Rathleague, Maryborough, William Clarke, Esq, Coroner for Queen's County, aged 78. Funeral will leave at 11 o'clock for Coolbanagher. Friends will please accept this invitation." Death registration Maryborough: occupation Gentleman and Coroner of Queen's county; cause of death "Natural causes to wit syncope."
The Irish Times, September 4, 1882:
"TO BE SOLD, the Tenant's interest in the Dwellinghouse, Offices, and Lands of Rathleague, late in the occupation of William Clarke, deceased, containing 202a 3r 21p I.P.M. held under lease from Lord Congleton (one of the best of landlords), for one life, now aged 45 years, at the yearly rent of £271 19s 1d.
The House contains 2 parlours, drawingroom, 5 bedrooms, kitchen, pantries, servants' apartments, &c., and is fit for the immediate reception of a gentleman and his family.
The Offices are ample for and suitable to the farm, all being in thorough repair.
There is also attached to the premises a good walled-in garden, pleasure ground, conservatory, &c.
The lands are under grass, with the exception of 30 acres (12[?] of which have been newly laid down), are ornamentally planted, well fenced and watered.
Gate-lodge and workmen's houses.
Rathleague is situated 1 1/4 miles from Maryborough, a station on the G.S. and W. Railway.
Purchaser to be approved of by landlord.
Every information can be obtained from, and proposals received up to 20th September next, by
Messrs. T. & H. TURPIN, Solicitors, Maryborough; or H.P.RHODES, Glenoak, Crumlin, County Antrim."

• Married: BEF 1837 in Ireland
• Note: Checking IGI for possible marriages (assuming they would have been married by license, rather than banns), the most likely is Eliza Drought, married 1836 in Dublin.

1. George CLARKE b: 3 Apr 1837 in Queens County, Ireland c: 6 May 1937 in Maryborough, Queen's County, Ireland
2. Isabella CLARKE b: 22 Aug 1838 in Queens County, Ireland c: 1 Sep 1838 in Maryborough, Queen's County, Ireland
3. John Parnell CLARKE b: 4 Jul 1840 in Queens County, Ireland c: 13 Jul 1840 in Maryborough, Queen's County, Ireland
4. William CLARKE b: 9 Nov 1841 in Queens County, Ireland c: 20 Dec 1841 in Maryborough, Queen's County, Ireland
5. Emily CLARKE b: 22 Dec 1843 in Queens County, Ireland c: 27 Dec 1843 in Maryborough, Queen's County, Ireland