I just worked on a machine with that same problem, today. I thought she wouldn't be able to serge with them, because when they flopped off the sides, it messed up the tension. But the boss just put some plastic cone holders on the spool pins, and they stayed in place pretty well. You should be able to get serger cone holders at any store that sells sergers. They're just those cone shaped plastic things that go on the spool pin.
The other thing to think about is the quality of the thread. If it isn't good quality thread, you won't get a good quality stitch.
With sergers, the thread has to pull straight off the top of the cone, or you'll get a wavy edge. So putting the cones behind your serger probably won't work, unless you can extend the wire thread guides.