A diesel generator will run on kerosene, but there are two problems that need addressing.
One is that the lower lubricity of the oil is not good for the pump, and in modern vehicle diesels this can lead to very expensive pump failure. But as pointed out above, an unsophisticated diesel engine may be OK. As Adam says, adding a lubricant such as motor oil, (or an additive such as those made by Millers) may be the answer.
The second problem comes when you try to restart a hot engine, and the oil evaporates before it can reach the injectors. This means you have to keep cranking the engine for a long time until it eventually starts; pouring water over the pump could help.
However, with a standby generator is the running cost the primary concern, or is it reliability?
I would use red diesel. It's not that cheap, and I do resent the tax that's payable on it, but at least it's not as bad as paying around 80% of the purchase price straight into Mr Brown's pocket.