Or on a day with good weather, depart him VFR and clear him IFR once he's seperated from inbounds (on RADAR or by any other means). It's a matter of choosing your words carefully before you do it, and let the pilot know what it implies, besides reducing a delay. Don't suggest it though.
Or still on a day with good weather the "own seperation" can be used if one requests it, and the other accepts. With carefull wording you can imply that the possibility is there and have the departure request it.