Possibly some papers in PRONI relating to the Gunning family:
D889/2/64 dated 1862/1863
Bundle of eleven documents including Copy Probate, letters receipts and accounts relating to the Estate of Elizabeth Gunning Intestate, William and Thomas Gunning Administrators.
I looked for a will for Thomas Gunning and for death notices in the newspapers but without success. Could not see death certificates for Thomas & Mary 1864 onwards (which is when death registration started in Ireland).
What denomination was the Gunning family? Have you looked for baptism records for Alexander and siblings? (Records may not be on-line).