Returns survive for the 'census' of 1787 and are held at the Kendal Record Office of Cumbria Archives Service. The Record Office reference is WQ/SP/C. They are transcribed in Vital Statistics published by Curwen Archives Trust 1992. ISBN 1897590008. There is a transcription on EdenLinks
Census returns are available from the usual sources for 1841-1911.
A transcript of the 1841 census of Cliburn [HO107/1162] is provided by Virginia Gretton. It includes the following names:
AICHBANK, BAILEY, BAXTER, BIRKET, BROWN, BYERS, CARRICK, CLARKE, CLARKSON, COULSTON, CREIGHTON, DALTON, DAY, DIXON, DOBSON, EDMUNDSON, FERGUSON, FURNESS, HALL, HARRISON, HENDERSON, HINDSON, ION, IRVING, JACKSON, LAYCOCK, LITTLE, LONGSTAFF, McDONELL, McHAFFEY, MAGEE, MALLISON, MOOR, NELSON, NICHOLSON, PEARSON, RAILTON, RAYSON, RICHARDSON, ROBINSON, ROBSON, RUDD, SALKALD, SANDERSON, SILL, SIMPSON, SOWERBY, STANLEY, STEPHENSON, STOCKDALE, THOMPSON, WAITING, WATSON, WILLS, WOOFE, WORKMAN, YARKER.
Transcript and index for 1851 has been published by the Cumbria Family History Society
and also in 'North Westmorland - An Index to the 1851 Census' compiled by David Lowis and Barbara Slack.