How to make outlet half-hot in this situation?
If there are just two 2-wire cables (excluding ground), it looks like this outlet and down-stream outlets are all switched, and no part of the outlets can be made always hot without new wiring.

To have a half switched outlet, you need either 3-wire cable coming from the switch (always hot/switched hot/neutral) or you need always hot line directly to the outlet box and then a switch loop controlling one half of the duplex.