What items and covenants can lead to multiplayer opportunities?
The name-engraved ring makes it easier to connect to other players. Basically, when you purchase the ring you choose a god's name to inscribe on it. While wearing the ring, you have a greater chance to be matched up with players who have the same god's name on their ring.
http://darksouls2.wiki.fextralife.com/Name-engraved+Ring