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Create a curtain with monofilament line. Each line is tied at a slight angle so they aren't perpendicular to the stage so your rain is not falling straight down. Focus ellipsodials on the monofilament curtain with a large break-up gobo in a rotater. This will give you the illusion of falling rain.
As a bonus, here is a link to a 282 page publication called Technical Design Solutions for Theater It covers SOOO many thinigs I am confident you will be interested in!
On page 151 is a description of how to build a space saving rain wall. Unless the theater owner absolutly refuses to allow you to use any water at all even if contained, this might be another option for you to consider?!
Take wood framing (2 X 2 is good) and hang it from a height adjustable rear truss as high as you need to so the front rows can't see the top of it. Extend them into the wings as far as required to make sure the audience also cant see the end.
Use more wood framing along the floor behind your floor lighting battens.
Drill 3/8" holes in it about every inch apart. (less holes for a lighter rain effect and more holes for heavier rain effect). Tie loops in your monofiliment lines (you will need about 400 + or - sections of line if your holes are 1" apart) large enough to comfortably insert a dowel into the loop. You will need to calculate your height. MAKE EVERY SECTION OF LINE, END OF LOOP TO END OF LOOP, EXACTLY THE SAME LENGTH!
Drop your truss to a comfortable working height and starting at one end, begin to insert your monofiliment loops through the 3/8" holes. As you insert one, as it comes through the top, insert a dowel through the loop. Continue one by one. Then do the same for the bottom. Raise the truss until taught and here is your monofiliment wall.
Configure your lighting as I described above and you have the dry rain effect!