My guess is midnight. Just so some of the posters here (not you) will know that it is a conclusion based on studying this case and not a feeling (are you listening Chrishope ), here's what I used to come to my best guess conclusion.
1. Midnight falls within the scientifically developed time frame based on digestion.
2. Patsy stated she usually got JonBenet up at midnight to potty (but said she didn't on the night JonBenet died; maybe she lied? maybe JonBenet was already dead by midnight?).
3. That Patsy stated she always turned on a nightlight and left JonBenet's door cracked so Patsy could hear JonBenet if she needed anything (but she didn't hear a thing that night; maybe she lied?)
4. That Patsy and John stated they got home 9-9:30 (depends on which version and from which participant you believe was accurate) then gave a list of things they did that imo would have put them in bed no earlier than 10:30 (and probably, for Patsy, no earlier than 11 PM).
5. That JonBenet would have never gone downstairs by herself at night and that she would have screamed bloody murder if some stranger tried to force her to do so.
6. And as DeeDee pointed out above, Melody Stanton reported hearing a scream around midnight.
Thank you. Very well explained.