The E key lets you set an event, ctrl+E copies an event and shift+E pastes it, and those are shortcuts you desperately need in general to work at a decent pace. Typically what you'd do is copy the event, place the tile, and paste the event. I do not believe that there is a simpler option supported by JCS, so if you want to do something more complex than placing single tiles, like paste a lot of contents of another layer into layer 4, you're out of luck. Perhaps a worthwhile feature request for MLLE.