A bit complicated, but feasible relatively quickly if the main character is alone or with deactivated followers. What I could suggest is to make the bed and the cover two separated parts. One to go on top of the other. This is how my tileset is setup.
However if the player goes to the tile below her head risks to be cut off.
So what I suggest is for the second part of the bed to actually be an event. It must obviously have the appearance of the bottom part of the cover. And its priority is "Below the characters". If the character goes to the tile below, the event is below the characters. If not, it's above. You want it to be a parallel event imposing a condition. When setting up the condition, go to script and say:
$gamePlayer.y === $gameMap.event(1).y + 1
If will make sure the event triggers if the character is at a position where it can be below the bed. If the condition is filled, I make him set ON a local switch (you can go for a regular switch if you prefer). Copy this page and paste it. In the copied page, make sure it triggers once the switch we set up is ON and it goes above the characters. Once done, go to your condition and instead of "===" type "!==" which should result in:
$gamePlayer.y !== $gameMap.event(1).y + 1
Finally, if the condition if filled, instead of setting the switch ON, set it OFF instead.
Then, it should work like this:
Finally, if you want more info on Script Calls, you can still check these: https://docs.google.com/spreadsheets/d/1-Oa0cRGpjC8L5JO8vdMwOaYMKO75dtfKDOetnvh7...
These are Script Calls for RPG Maker MV, but they still work on RPG Maker MZ so you should have no problem making use of these.
Hope this helps.