I'm getting some more ideas here. Thanks.
Does anyone know if a pancake shape coil would be better than a long, slender coil for this application (with the coil at the bottom and the magnet swinging over it)? I don't know what gives the greatest magnetic field strength near one end (pole) of those two kinds of coils, if there is any difference. I can't use a ferrous core because then the magnet will gravitate to the core and hang up there. I think I pretty much have to use an air core, or ferrite core. Also, I saw one reference that stated that the core diameter of the coil should be the same as the magnet, but gives no reason why.