Can suspensions be separated by centrifuge or by separatory funnel?
If you are indeed dealing with a proper suspension (not a colloid and not a solution) then centrifugation should always work to separate the components. It may be that you need a very high rotation speed or a long time, but you will manage to get the solid particles to the bottom of the tube and the clear liquid above.

A separatory funnel is a bad idea for a number of reasons. For one, you don’t know how long it will take for the components to separate. For two, you will probably have difficulties removing the solid portions; they might clog the opening or they might attach together not intending to go through at all. Finally, you will always get some liquid together with the solid fraction in a separatory funnel while you should arrive at a much better dryness with centrifugation.