Not sure why you would bother...
Subsonic rounds tend to do better in 'under-bore' (I know this is not a proper term) cartridges, like the classic .22LR or to a lesser extent the .308. (.300 BLK if you are cool).
The .243 is an 'over-bore' cartridge, so unless you have a custom bullet which is exceptionally massive, and an exceptionally fast twist (not a regular 1:10) you will probably get bullets that are not quite subsonic, or ones that 'key-hole'. Not ideal.
Then again, I've not tried it. This guy has: