unless you want to fade each seperate item delayed a bit in/out (which is not possible to my knowledge) you should be able to do it like this:
Your inventory (or later settings, etc interfaces) need to have position:absolute set. The X is set to 0 and the Y coordinate should be set to a value that only one pixel line from the top side of the interface will be seeable (you can make it transparent in the graphic later, but you need something to detect the mouse).
Create a button in the interface and set it as an "action area". No image needed for that button. The button polygon needs to be covering the 1px area at the top side of the interface (don't have to be that acurat because it only will conroll the slide in)
In the mouse-enter action of that button add an "execute script" action part and add this:
Interfaces["inventory"]:to(1000, { InterfaceOffset = {x = 0, y = XXX } })
where 1000 is the time in ms it takes and XXX should be the Y-position of your interface when visible. "inventory" has to be replaced with the name of your inventory.
In the INTERFACES "action on leaving" action (in interface properties) execute a script like above but with Y= original position.