Don't know if you've found anything since asking your question, but here is what I have on Edneys in Ireland. Sources are listed at the end.
1602 - Capt. Walter Edney was sent to Spain as a spy against Hugh Roe O’Donnell. [O’Donnell was an Irish earl who’d fled to Spain in 1602 and died there later the same year.] Edney was captured and imprisoned until 1603-04.His brother, Thomas Edney, gentleman, had remained in Ulster and was there still.It was unknown to the chroniclers where the Edneys had come from or what circumstances had brought them.However ...
10 Sep 1602 - Walter Edney was described in a letter from Captain Henry Moyle [Boyle?] in County Cork, preserved among "the Carew Manuscripts", commending as follows: "... Walter Edney, lieutenant to Harvie, a person of good judgment both in land and sea service, having had in former times the charge of a captain in fleets under Sir Francis Drake to the Indies and others, and of long continuance both since and before in land service, and besides well known to the Veador and to all the Spanish captains that were at Castlehaven and Baltymore. ..."
15 Oct 1602 - From Mr. Boyle in Cork: "I have sent one Walter Edney, lieutenant to Captain Harvy, into Spain. This next month I expect his return, when your Lordship shall have certain intelligence of Spanish affairs. If the merchants which came last from Lysbone may be believed, I am little beholding to that nation, for one of them was in trouble for buying a Spanish Chronicle, because it was for my use; which makes me to apprehend some fear that Lieutenant Edney.. might be barbarously used, and Don Juan's promise little regarded. I pray you (understanding of certain Spanish captains lately taken in England) that stay be made of some one of them until his return. This I write, more out of providence than any opinion I have he will be stayed; nevertheless I may not omit any care due unto those that hazard their lives and goods (as he doth) to serve the Queen."
30 Apr 1604 - Capt. Walter Edney was granted a lifetime daily pension of 4 shillings “for his services in Spain ... wherein he suffered imprisonment and other ill intreatie, to his utter undoing”.The granting of the pension was made at the order of Sir George Carew and does not mean that Edney’s “undoing” came through any fault of his own but through suffering at the hands of the Spanish.
1606 (approx.) - Capt. Walter Edney and Thomas Edney, gentleman, his brother, were first patentees of 1,500 acres in the precinct of Clogher, County Tyrone, called Ballyloughmaguiffe and created into the manor of Ridgeway with a court baron.
20 Jan 1613 - Walter and Thomas Edney let or leased Ballyloughmaguiffe to four O’Neills described as “meere Irishmen”.The Edneys “afterwards distributed the several parcels of their lands to the natives hereunder named ... [Irishmen of various surnames]”. The grave of Mary, Wife of Captain Walter Edney, is in Dublin’s Church of St. Nicholas with internment dated 14 November 1?39 [second digit illegible, but the date presumably is 1639] and with arms described as “Sa. a lion's bead erased betw. three crosses pattee ar.”Where Thomas Edney spent the remainder of his life has not been discovered.
I am not an Edney descendant. I found this information while pursuing a possible connection between them and the Widneys, which I believe now not to exist.
1."An Historical Account of the Plantation of Ulster at the Commencement of the Seventeenth Century, 1608-1620", Rev. George Hill, Belfast (1877), pp. 264, 542.