The horizontally layed out harp is covered with these rain catching disks, each on a flexible wire. Below each disk is a small metal hammer element. When a raindrop hits a particular disk, it in turn strikes the area of the string below it.
Alternately long rain catching picks, picture a long pineapple
leaf shaped thing, could simply be arrayed around the harp each reaching into a particular string, plucking it rather than striking it when hit with a rain drop. You might have to play around with leverage points to get a solid pluck but I think it could be done.
The harp would have a standard tuning and the notes would be random, not playing any particular tune.
You could have the strings all tuned to major chords or even notes that create melodic movements, but I think just having random notes playing nothing particularly musical would match the rain better.
The linked example has reverb which could be easily achieved with springs attached to the resonating chamber within the harp body.
ADDENDUM: Thinking of how to slow this down, instead of panels striking or plucking a string with each drop, little spoons or cups could take some measure of time to fill up and when heavy enough, push down and pluck or strike the string. I think I like the idea of these being activated more slowly to be more relaxing.