Neighborhood Watch Partnership Act of 1999 - Amends the Omnibus Crime Control and Safe Streets Act of 1968 to authorize within the public safety and community policing ("cops on the beat") program assistance to unincorporated neighborhood watch organizations approved by the appropriate local police or sheriff's department for the purchase of citizen band radios, street signs, magnetic signs, flashlights, and other equipment relating to neighborhood watch patrols. Authorizes appropriations.