How to level up staff units fast?

Give them the Savage Blow seal, and a staff, and have 3 tanks without their weapons, and have fun leveling the healer up slowly but painfully.

If you have the Savage Blow SS, equip that, and bring a mixture of tanks and dancers into one of the maps with a steady stream of enemies. Set up in a corner with your healer safe away from the action, but where they can still deal damage/heal. The enemy will get easier to kill when they accumulate chip damage, and you can heal the tanks for extra SP/XP. (Unequip the tank with a weapon, though.) Not necessarily the fastest, but it'll allow the healer to build up enough SP to either get the Wrazzle refine, which helps with this even more, or the Savage Blow C-Slot. Rinse and repeat until your healer is built.

shards and crystals, then with that sp give them a pain staff and pair them with dancers

Most of the time, you'll want to wait for Magic Training maps as armored units have non-existent Res. Have plenty of Dancers to go with them.

Alternatively, using Shards and Crystals will make them reach level cap easier, but you'll miss out on extra SP by defeating enemy units.

One of your better uses for shards and crystals. Now that SP gains from level-ups have been boosted, levelling to 35 should be enough for a wrathful refine. If you're not planning on one, you might want to level the healer well past 20 as a 4* before promoting. That should give you at least 1500 SP just from level-ups.

Another method I like to switch out with what others have suggested is just to pair the healer with another unit I also want to level/ SP grind.

Unequip the healer's weapon, combine the pair with two dancers and auto-play a map the killer can survive, but will take occasional damage (or heal the 1 point of 'damage' they incur from levelling up).

I'm not sure if it's any faster, but because it's knocking out two units at once, it feels like less of a grind for me.