Base Resistor for 2N3904 help
It looks like you have something like this:



(Original image source from ZappBots)

You don't specify what your control voltage is (the one you'd use to source current to the base) but in general, you could choose a value for the base current equal to a tenth of the load current and that way, you could choose a base resistor:

$$R_B=\dfrac{V_{control}-0.7}{I_B} $$

Since the coil needs 16.7mA, say you choose \$I_B\$ = 1.7mA. For example, if the control voltage were 5V, then \$R_B\$ would be:

$$R_B=\dfrac{5-0.7}{1.7\text{mA}}= 2.53k\Omega $$

Something close to that should work.