Again with thanks to Elisabeth Cunnington's work, I am able to add to my list many (apparently unconnected) references since the 12th century which we have separately found over the years of research:
P H RENNY DICTIONARY of BRITISH SURNAMES pub 1958 states:
Cunnington is Pagan/Richard de Cunington, post 1193,Leics.
1210 Curia Regis Rolls, Cambs./ From Conington, Cambs/Hunts.
WILLIAM CONINGTON (Edward IV) A Fisher of Nottingham was prosecuted in 1467 for playing at Tennis, a game prohibited to serving men and labourers (Records ii,365).
WILLIAM CONYNGTON (Henry VII) Was a Chamberlain of Nottingham in 1486-7(Records iii,459), and one of the Sheriffs in 1490-1 (Ibid iii,459).
WILLIAM CONYNGTON (Henry VII) Fishmonger, was sued in 1496 by Edward Wilson, Hatmaker, for rent of a messuage called "The Crane" (Records iii,469).
RICHARD DE CONYNGTON (Edward III) Appointed Vicar of Lowdham on 22 March 1372; had resigned for Hospital of Freforth, dioc. Cor. by 1393. Torre MSS (Lowdham Church,3)
RICHARD DE CONYNGSTON (Henry IV) Prebendary of Norwell Palishall 1400-13, buried at Southwell, was also a Prebendary of Beverley, Chancellor of York, and Rector of Hickling Le Neve's. (Fasti iii,441).
WILLIAM DE CONYNGTON (Edward III) Presented by the King to the Rectory of Barton in Fabis, to which living he was instituted on 01 July 1357. He held it until his death, and was succeeded on 29 September 1398 by Richard Arnall Torre MS (Barton)
WILLIAM DE CONYNGTON (Edward III) Presented to church of Barton by Nottingham on June 28 1357, by reason of Lenton Priory being in King's hands through war with France. Pat. Rolls(1357), 570.
WALTER DE CUNNINGTON (Edward I) CUNIGTON Served on ino. p.m. at Ratcliffe on Soar, 1294. T.S.Inq.P.M.,ii,59.
BEDFORDSHIRE HISTORICAL RECORD SOCIETY
Vol 1 p 237 BEDFORD EYRE 1202 Mem 6, Half Hundred of Buckslowe,
Mentions William de Cuninton in a case of wounding/violence.
Vol 2 p 247 BEDS KNIGHTS IN SERVICE IN WALES 1244-5 Mentions Richard de Cunynton, serving for Robert de Gunilles, service done to Henry, King of England.
Vol 9 p 13/14 mentions a Constance who remarried a Bernard de Bruce, she was holding lands at Conington Hunts as a wedding gift.
Vol 9 p 181/2 mentions a meadow at Conington granted to Abbey de la Pre, NTH.
VICTORIA COUNTY HISTORY of HUNTINGDON:
Geoffrey de Conyngton, an outlaw, whose lands in 1294 were
claimed by the King of Scotland (presumably as the Earl of
Huntingdon, his overlord) Geoffrey was the son of William, who
was the son of Henry de Conyngton. He held the lands of the
Leper hospital of St Margaret, near Huntingdon, which had been
endowed by David I King of Scotland and Earl of Huntingdon
CATALOGUE of ANCIENT DEEDS in the PRO Vols 1 & 3, pub 1890
(In British Museum North Library)
Robert de Conigton (de Conington) Knight, or de Cuninton
Knight, appears as a witness to contracts concerning lands and
services in Huntingdonshire about 1267
Thomas Conyngton listed as holding lands in Grafham, in a
document dated February 6 14 year of the reign of Henry IV
J Foster Alumni Oxonienses 1500-1886 8 Vols pub 1887-92
Richard Conyngton, a Franciscan Friar and Theologian, who died
in 1530, and is also described in the Dictioary of National
Bibliography.
J & J A Venn Alumni Cantabrigienses 10 Vols pub 1922-54
John de Conington, scholar of Kings Hall, Cambridge. He died
July 10 1349, perhaps of the black death ?
Alexander Connington 1483-4 "was given grace for keeping his
terms"
Exton Church Records
Nicholas de Connington, priest at Exton 1307, whose patron was
Sir Bernard de Brus, Lord of the Manor of Conington. Nicholas
is also listed in 1305 as having as another patron the Priory
of St Andrew, Northampton.
Roger de Conyngton is mentioned in 1318, his patron being Sir Bernard de Brus.
Peter de Conyngton is listed in 1328, with his patron the Priory of St Andrew, Northampton ...apparently there was a connection between Sir Bernard and this Priory.
Wills from 16C
When we reach the 16th century, there are Will records, and the
first (often incomplete) parish registers of baptisms,
marriages, and burials. In 1538, Thomas Cromwell, Vicar General
under Henry VIII, ordered that parishes were to keep these
records, but not all parishes did so.
Some early Wills are :
John Conyngton of Holme, near Conington dated 1507 (16 Vol II)
Thomas Conington, Husbandman of Conington, dated 1571 (16 Vol XIV)
Bernard Conyngton, Husbandman of Conington, dated 1596 (16 Vol XV)
An early parish register is Thorpe Achurch, Northamptonshire :
1561 Jas Connyngton married to Annes Hensun (FAMILY 94)
1598 Cath Conington married Jn Dodes (FAMILY 12)
1599 Wm Conninton married Cisley Rowel (FAMILY 2A)