I'm not sure on when conures normally wean, but I do know you never force them to wean.
Keep offering that hand feeding until your bird refuses it on a fairly regular basis.
There's no separate formula, but some people offer warm mashed normal food by hand or spoon.
Stuff like soft warmed sweet potato, oatmeal, warmed unsweetened applesauce, even moistened pellets.
The soft warm food fed by you is called comfort feeds, and helps a baby feel safe and comforted.