No there isn't any colours beginning with "ö". Not even designer-colours such as light hyacinth blue or yellow ochre for example, are written with "ö" as initial.

Hallo, Glaub ich nicht, aber " Ölfarbe" kann man nicht als eine Farbe bezeichnen.

In case you don't think of "Ölfarbe" (oil paint | which describes the consistency, not the appearance) then I would say there is no "natural" color starting with "ö". With "unnatural" I mean that there is always the possibility to add some attribute to a "natural" color like red, green, blue, ... For instance one could talk about "olivgrün" or such things. Well possible to find a characterization which begins with "ö" but people would not use that naturally/frequently