Soldering Caps Across Motor Terminals
The cases are generally made of steel, and steel is difficult to solder to.

Sand a spot on the case with fine sand paper, and use a larger soldering iron (a little 30W iron won't give enough heat.)
A soldering gun (like this one) will probably do a better job than a normal pencil iron.

When I've had to do something like that, it has usually taken several attempts to get a good joint.

Sand, solder, let cool, pull on wire.  If it comes off, do the whole thing again.



There is acid core solder available.  That would work better for soldering to the motor, but you must be sure to remove ALL of the flux afterwards.

I've not tried it, but if you have many of these to do, then you may try this:


Sand a spot on the motor with fine sand paper.
User a soldering gun and acid core solder to tin the sanded spot on the motor.
Clean all traces of the acid flux from the motor.
Using a second iron (that has not been in contact with the acid flux) solder the capacitor to the tinned spot on the motor.