Marriott changed their policy early this year and now the rate rules for Government rate rooms generally state "Only eligible to government employees on official business." It appears that this was mandated across the board for all MB properties, but with a carve-out to allow properties to also offer Government leisure rates if they wished. This policy change has caused me to cut back significantly on Marriott stays for both official and leisure travel this year.
I occasionally see Government leisure rates offered, but they're rare. I also don't know of any way to specifically search for Gov leisure rates.