Firstly I would tell them they will have to move when the lease is up.
I would then offer $6000 if they move in January, $5000 in February, $4000 in March etc, no bonus left by July.
This is a great idea. Why not make it $7K if they leave in December. If they don't jump at the money in December how long into January before your settlement? I think the stress of not knowing if they are going and not knowing if you have to quickly find a place to rent would be awful.
What date in January is your deadline to KNOW they are moving? What is the date that you cannot wait any longer and must find a rental for yourselves? You could end up with them giving notice a week after you have been forced to sign a lease for your own family.