This could obviously be done with flash/actionscript and there is likely a few players out there for this. It would be relatively simple to code such a thing though with basic controls and you would merely need to check if the current song has reached the end, possibly have a short delay and then play the next song in a list.
If flash isn't your thing HTML5 is fully capable of doing this as well. Though you would cut off your system to anyone not using a modern browser but that's your personal decision.
When I get home later tonight I could always write up some code if you somehow feel you can't research any of this or just have no clue on how to begin coding either solution.
"Given billions of tries, could a spilled bottle of ink ever fall into the words of Shakespeare?"