Maybe a little explanation would be in order... lol, sorry. The reason I view this as a "Poor Man's" option is for sake of the lack of cost needed for supplies.
1. A shoebox sized plastic tote.
2. A tank that will accomodate a screen top.
3. A fitting screen top.
4. An ability to drill a small hole through real glass.
5. Either a funnel or a rubber tubing section.
6. Super glue and aquarium glue.
7. A bucket to collect drainedwater.
8. Saran wrap and tape(for modifying the screen top).
I would love to try this. It would require YOU to pour the "rain" by hand, but is that so hard?
Just as comment, you really need a second drain hole somewhere in case the first one become clogged so you don't burn out the pump and/or flood the rain chamber (possibly drowing poor swimming anurans).
Because of the hole drilling it may be cheaper in the long run to simply purchase a utility sink... with the shoe box on the top, you have to play with pump flows to keep from flooding the box while still getting "drip" through the maximal amount of the holes.. It is easier to use a wide shower head or water can head.
With the utility sink, you can build a cage extension upwards using smaller diameter pvc tubing and cover the top with screen (the rain emitter can be inside or outside as you choose) and the sides with plastic.
The last rain chamber, for my Bumble Bee toads, I used a 10 gallon aquarium with one shoe turned upside down with holes drilled in it in the bottom of the box, so it wouldn't float, to hold up another plastic shoe box with a fine screen bottom (larger holes cut into the bottom of the shoe box and screen siliconed in). Between the shoe boxes you can put a spacer of some sort to allow water to pass freely. The shoe box lid had small holes in the lid that I melted through with a wood burner (you could use a 1/16" drill). I used a small pump from graystonecreations.com to pump water from the bottom ot the tank onto the top of the shoe box and water softly dropped onto the toads. Excess water ran back off the top into the tank. Could be done with 2 larger sweater boxes--one larger than the other so the large one would hold the water for pumping and the smaller one would have the top and fit into the larger one to keep the water completley contained.