Since you can only unwrap Store items on the map field you're standing on, you have very limited ways to unwrap one over an unwalkable object such as the Potted Flower. As you pointed out, you can't use the logout & login trick there because the stairs field is walkable and the character would go upstairs when logging back into the game. Of course, the situation would be different if it was a ladder instead of stairs.
All other ways I can think of are dependent on map elements that move/teleport characters even if the destination field is occupied by an unwalkable object, such as doors, stairs and ladders, but none of them apply to the place in question. Therefore, there is no way to unwrap a Store item on a Potted Flower placed on the desired spot.
PS: You would be able to do that if you were a Cip member, but they probably wouldn't allow you to rent a house with an official CipSoft Member character. ;)