I am researching my family from Osprey, Grey County, Ontario. I show them appearing on the 1871 census and not on the 1881 census. I assume they died during this time frame. I cannot find them in any local cemetery. My question is this: I have a 10 year time frame on their death dates. Is there a way to have a lookup done (by the government or by a newspaper) by their surnames as I don't have a death date?

They could have moved... but in answer to your question the government does not do lookups and most newspapers likely don't either. They may engage in a search on your behalf for a fee but you can do this yourself. All deaths from 1869 onward were required to be registered with the government. These registrations are available for public viewing if the death occurred more than 72 years ago and can be accessed at any Canadian library or any LDS Family History Center worldwide. See our page on Death Records