In a situation like this, I have created a notehead set using the quarter rest and eighth rest as the noteheads for a quarter note and an eighth note. After the notes are entered on the staff, the rest noteheads are selected and the stems hidden in engrave mode. Playback of these notes should be suppressed.
Edit: To have the rests appear at the correct vertical positions in both the score and the part, create two-note chords using the rest noteheads. In the part with the property scope set to locally, hide the rests for the score by setting their custom scale to 1. Then hide the rests for the part in the score. If the rests in the score are outside the staff, the ledger lines can be hidden in engrave mode.