Dr. Conrad Murray's girlfriend is begging the court to let him out of jail pending his appeal ... claiming he's a "good father" to their toddler.
Nicole Alvarez -- who played the femme fatale during the trial -- filed a declaration of support for Murray today ... in which she says if Murray is released he will live with her and their 2-year-old son in Santa Monica.
It's not the most powerful or emotional letter. Alvarez says, "Dr. Murray is the father of my child" -- and adds ... he "has been our primary source of support."
It's unclear how much support Murray can provide now -- considering his medical license has been revoked.
Murray's hearing for bail pending appeal of his manslaughter conviction is scheduled for tomorrow morning in downtown L.A.