SCT Controller reported that when LAX is landing east; there are no specified procedures for handling SMO arrivals; causing at times a lack of coordination regarding arrivals and departures from SMO. That was the case for this event.

Narrative

[This regards] LAX east traffic and SMO [traffic] landing Runway 3. In this configuration there are always problems and confusion. Three different areas are involved: LAX Arrivals; LAX Departures; and Burbank. I've been in this facility 13 years; all of it in either LAX Arrivals or BUR and it's always been a problem that nobody wants to address. Each time this configuration occurs everybody starts from scratch trying to figure out how to handle the conflicting approaches. In this particular event; LA [Center] (due to their arrivals) refused to take SMO arrivals that weren't on a visual approach. It was possible; with much effort; to vector the SMO arrivals to a lower MVA and get on a visual approach. Malibu sector which would normally take the handoff didn't want to until the aircraft were on the visual approach. The SMO arrivals I worked were; therefore; displayed on Malibu's scope so they knew they were coming but the handoff not made until the aircraft were actually on the visual approach. When this occurred with Aircraft X; unknown to me there was an opposite direction SMO departure. After several traffic calls Aircraft X saw and was able to maintain visual separation with Aircraft Y.[Recommend] having definite procedures for these conflicting approaches rather than 'winging' it every time this configuration occurs.