Yeah, funerals don't usually have guest lists, and definitely not sign-in books! Most of the time a notice is put in the paper stating the time and place and whoever comes, comes. Or it would say "the family is holding a private service," in which case you can't come unless you're invited, but then you'd be a member of the family.
You could get around this, however. For instance, perhaps the deceased person was into a certain cause or whatever. Maybe the widow would have a petition for something that he was very committed to at the funeral, asking people to sign it. Or perhaps they put one of those "instead of flowers, the family has requested that donations be made to ___" requests in the paper, in which case you might be able to get a list of people who donated. Or if there was a lot of controversy surrounding his death, perhaps the police would be at the funeral checking IDs.