EDIT: Corrected my repeated use of 'Shillingston' instead of 'Shillington' and added some other details re: the origin of the family and earlier generations.
The Shillingtons were a prominent Methodist mercantile family of Portadown, County Armagh. They aren't in Burke's Family Index, but nevertheless lived for several generations at Tavanagh House, Portadown, and produced some notable individuals:
Anthony Drummond Graham Shillington (1943-) of Glebe House, Shalstone, Bucks., a director of Stowe School Ltd 1991-3, and of Buckingham Winslow and District Citizens Advice Bureau 2005-9.
His father was (Robert Edward) Graham Shillington (1911-2001), of Orchard Hill, Craigavad, County Down, educ. Sedbergh, Clare Coll., Cantab. (B.A. 1932), Chief Constable, Royal Ulster Constabulary 1970-3, K.B. (1972), C.B.E. (1970) by his wife (m. 1935), Mary, dau. of - Bulloch.
R. E. G. Shillington s. (yst of 6 ch) of David Graham Shillington (1872-1944), of Ardeavon, Killycomain Road, Portadown, educ. Methodist Coll. Belfast, Rydalmount Sch., Maj., 9th Royal Irish Fusiliers, a merchant in Belfast, M.P. for Armagh and later Armagh Central, Minister of Labour 1937-8, P.C.(N.I.) by his wife Sarah Louisa, dau. of - Collen.
He s. of Thomas Primus Shillington (1831-1889), of Tavenagh House, Portadown, J.P., by his wife Mary Jane (d. 1915), dau. of - Graham.
He s. of Thomas Averell Shillington (1800-1874), of Tavenagh House, J.P., by his wife Elizabeth (1799-1870), dau. of John Johnston, of Lurgan.
T. A. Shillington s. of Thomas Shillington (1767-1830), who completed Tavenagh House just before his death, by his wife Sarah (1762-1847), dau. of Nicholas Averell, of Ballinderry, Co. Derry (cousin to Dr Averell, Bishop of Limerick) by his wife Hannah.
Also of this Portadown family was Thomas Shillington (1835-1925), owner of the Castleisland Linen Co., chairman of the Irish Land Committee at its formation in 1883, a Liberal and independent nationalist political candidate, P.C. 1911, P.C. (N.I.) 1923. His father- Averell Shillington (1802-1897), owner of the Castleisland Linen Co., and from 1832 to 1890 superintendent of the Methodist Sunday school at Portadown- was a younger brother of Thomas Averell Shillington (as above).
In the volume 'Christian Thoroughness: a memorial sketch of T. A. Shillington' is written: 'The Shillington family is of English descent. Two brothers came to Ireland about the year 1658, being encouraged to do so by Lord Conway, and took up their abode at Aughagallon, in the county of Antrim. Their immediate object appears to have been to execute extensive works at Portmore for the celebrated Jeremy Taylor, who was appointed to the bishopric of Down and Connor. Of the intervening members of the family little is known until we come to [(Thomas Shillington (1767-1830)]'.