I have a bed that looks like this, doesn’t have legs.
I was looking at bed risers, but they’re aimed for beds with legs. Also, the risers make the bed rise too high for my needs.
I only need to make the bed rise for about 2-inches so I can use an overbed table like .
If the 2x4 width (about 1.5) is too small, 2x3 lumber is common. Get a bunch and screw two boards together to use three 3 inch (actually about 2.5) so that you don’t worry about the board tipping.
Since your current frame is legless, i’d probably do a decent sized frame underneath so not just supported at corners.