ScotlandsPeople.gov.uk does allow you to search the 1881 Census by only inputing an address or partial address. If you can find the house then obviously you could then search for the same family on the 1871 or '91 records. If they owned the house then you might even find it in a will.
Depending on the type of property, there might be some info in trade directories or tax records and there's also the electoral roll. If the house is in Glasgow then you could visit the archives at the Mitchell Library:
http://www.glasgow.gov.uk/en/Residents/Leisure_Culture/Libraries/Collections/FamilyHistoryThe only other suggestion I can make is to try searching for the address on Google.co.uk.