Hi
Does the following help, not sure if it is the Horse and Tiger, but only one showing up on census.
1861 census
JENKINSON, Joseph Head Married M 37 Joiner Inn Keeper
Kimberworth Yorkshire
JENKINSON, Maryan Wife Married F 38 Yorkshire
JENKINSON, Joseph Son M 15 Coal Miner Yorkshire
JENKINSON, Harison Son M 11 Yorkshire
RG number: RG09 Piece: 3508 Folio: 10 Page: 14
Registration District: Rotherham Sub District: 3 Kimberworth EnumerationDistrict: 15 THORPE HOSLEY SOUTH HILL Ecclesiastical Parish: Thorpe Hesley
Civil Parish: Kimberworth Municipal Borough: Address:
..., Thorpe, Kimberworth, West Ridney
Kind regards
Joy