I've said this in another thread-- but I've made support traps to bait FBs, and the FBs don't destroy the supports. The come up and destroy every door next to the support, but leave the support. I think the support thing might just be a good idea that's based on previous versions that doesn't work.
But a support trap isn't your only guaranteed kill. An obsidian trap is also a guaranteed kill. Some modification of the building destroyer pressure plate trap can be made to make an automatic obsidian trap:
#water #
#bbbbbbb#
#magma #
#bbbbbbb# notice that that last "b" on this line is a separate bridge from the first 7 bs--- this is to prime the area behind the door below with magma
#####bb__^+_#
_____/
The trap needs to be longer than this, because there's going to be a delay, and you don't want the beast escaping the trap. You have a basic trap hallway, with magma dripping down from above, but held behind a door. Immediately above is magma held in place with a retracting bridge; and above that, water held in place with another retracting bridge.
The only automated part needs to be the pressure plate and the lowest bridge, to trap the beast. The rest can be done at leisure with levers. If you really want to automate the way it goes off, it's possible. You'll need an extra pressure plate, linked to both magma bridges and to the water bridge, which is set to go off on 1+ magma. Just be sure to build the magma bridges BEFORE you build the pressure plate, and the water bridge AFTER you build the pressure plate, so that the water drops a tick after the magma.
Reloading the trap can't be automated. You'll need to dig out the obsidian and install a new door. Magma reload isn't pictured, but can be added on to the magma level, which is inaccessible to forgotten beasts.
If you really, really want to get a FB in a cage trap, and, as I suspect, they don't target supports, you're going to build a complicated, one use trap:
from side:
bbbbbbb_^X_#
/# ^^^S
top:
###
bbbbbbb_^X #
###
top, z-1:
^^^
/# S
^^^
In other words-- you have to make an artificial cistern to hold water, held up by a support. A pressure plate is build on constructed floors, such that it triggers the support when the cistern is broken into. Not pictured is the fact that you need a long passage of constructed floors held up only by the support-based constructions, because there's going to be a delay. One z-level below this long passage, you have cage traps-- not directly underneath the constructed floors, but on either side, because when the floors collapse, the'll destroy anything underneath them.
So when the FB penetrates your artificial cistern, it triggers the support, and drops the beast. Since the beast isn't getting anything collapsed on it, it suffers falling damage only, but the dust knocks it out, and the beast will be scattered a square. 6 of the 9 squares it can be scattered to contain cage traps. Not perfect, but I'm pretty sure it's the best that can be done.