I used to use a Heathkit function generator hooked up to a small NAD integrated amp (3020 or 3155) amp to power the driver. Now I've downloaded a function generator/test tone app to my iPhone and use that to drive the amp into the driver.
Nice part is I can easily vary the frequency with a nice digital readout, plus I can set the output to a fixed out on the iphone, then vary the signal power to the driver through the amp's volume control.
When you do this, the voice coil is nicely centered by the magnetic signal flow in the voice coil. With the surround already glued to the cone (back or front), its then easy to temporarily clamp down two opposing sides, then two more (or thirds if you like) while the tone if running. After clamping, test again to be sure you're centered - I've found I need to hold the driver in free air so that table vibration and resonance doesn't cover up any distortion or noise. I use medium to large binder clips or alligator type clothes pins.
Once you're satisfied you're centered, then take off one clamp and glue a section of surround to the frame. Once that's done, reclamp with 1-3 clamps, test again and adjust the position of the surround (usually not needed), then move around the driver till all sections are glued and reclamped. All along the way, the testing has confirmed at each step I'm still centered at any frequency I use.
BTW, if using binder clips, they are strong, so you might consider putting a sliver of thick card stock under it to spread out the force, otherwise you can get some dents in the outer frame part of the surround. If you're putting on a gasket on top of that part, may not be needed from a cosmetic standpoint.
I like this method because I'm concerned that trying to glue without clamping may angle the voice coil and you would't know it just by feel with some wider gaps.
As for playing signal while the glue is wet and that centering the surround, I would have to think the glue has to be quite fresh and wet to be able to move any bit laterally, otherwise once it gets tacky, only finger pushing and pulling is going to effectively move the outer surround edge on the frame IMO.