Slingbox 350/500/M1 are all DHCP or nothing for network setup. If the Cisco ASA can't support DHCP reservations, you have a bit of a problem. You might be able to add another router (e.g. a consumer router) that does support DHCP reservations and port forward to that which then forwards to the Slingbox, but that's adding extra complexity.
Otherwise you need a Slingbox that's older than a 350/500/M1, which are getting less and less support as Sling Inc. moves forward.