Sorry but as Ghengis says, the only way to log any time whatsoever would either be with an instructor or in a multi-pilot aircraft. Your PA-28 only requires one pilot . The only time you could have two occupants logging time would be when one was logging PIC as instructor and the other logging Pu/t or (PICus for a successful test).
Anyone looking at your logbook will immediately spot P2 time in a PA-28 and disregard it.
In the past, when I've flown memorable trips I wish to record, I just enter it in my logbook as "for info only" in some suitable column.
Anyway, why would you want to claim P2 time? If it's for recency then you're obviouslyon dodgy ground. Likewise, if you're hour building towards CPL mins.
Enjoy the flying and log P1 time only from the LHS.