I think you will need some kind of latch, that unit will be too heavy to be held in place with magnets, once you start hitting bumps, it will probably release and drop down on you.
I'd probably suggest a design based on a house door lock, whereby you have a bevelled slider and striker plate. So the slider fits into a striker plate and socket on the monitor, and has the lower side bevelled so that you can just push the monitor up into the position to latch it, rather than having to use both hands to hold the slider back and push the monitor up.
As for where to find one? Not too sure, you may have to check out some cabinetmakers supplies, and find something that is close and small enough, but can be cut and molded into a housing. You could probably source a small latch like the ones used to hold back walls on dollhouses or the like.
Or alternatively, go to a wreckers, and pick up a glovebox and the locking pin off a car, and mould those to suit