Earlier quoted context omitted.
Use a p2p sync program like BitTorrent sync or an alternative. Skip the cloud. It's just someone else's computer.
But it's someone else's computer that is pretty much guaranteed to be available, and probably more secure than mine.
Also, you're putting too much faith in other people's computers.
That said, most of these password managers use really strong encryption so having your password file exposed isn't much of an issue.