How to make an effective electromagnet?
I'd aim to maximize the force between windings and magnet - this should impart maximum force onto the speaker diaphragm. Magnetic Force exerted by a solenoid is: -

\$\dfrac{(F_M)^2 \mu_0 A}{2 g^2}\$


Where Fm is magneto motive force in ampere-turns
A is cross sectional area of solenoid or coil
g is the gap between solenoid and poles of iron (in your case the magnet)
\$\mu_0\$ is 4\$\pi \times 10^{-7}\$


It's not 100% clear to me how g would be measured because normally is would be the gap at the end of the solenoid in the direction towards a piece of iron. Nevertheless, the clues in the equation above tell you that the cross sectional area of the coil and the number of turns will play a dominant role in getting more force onto the speaker cone/diaphragm.

If it were me I'd just buy a speaker!