For very low power applications like yours, it doesn't make sense to use a full size antenna such as the classic quarter wave or half wave types. These are simply way too big. You need to use a structure that lies halfway between a classic antenna and a pcb tank circuit and what I am thinking of is simply a leaky coil. A wire coil that resonates (or is resonated with parallel capacitance, ie. a tank circuit) will also radiate and if it is a larger size than would normally be used on a pcb, with widely spread windings, perhaps this would be a suitable antenna. Its very much like a smaller version of a helical-loaded monopole or dipole. How big can it be? Several inches of length would be sufficient, I think.