Unless you want to wit for the weather to be just right, you could build a rain chamber. A friend did this to get his whitelips to breed..... he ended up with 800 young frogs.
This is heaps easier if you've kept fish previously as you'll have most of the gear lying around.
Pretty much get two tubs (one larger than the other), drill/melt holes in the base of one end of the smaller tub, and place it inside the other tub. A small fish tank pump is place in the bottom of the outer tub. A piece of tubing connected to the pump outlet to a fish tank spray bar which is then connected to the lid of the inner tub. Turn the pump on and play around with water levels, and there should be a small pond in the bottom of the inner tub and a larger volume around the pump in the outer tub. "Rain" from the spray bar in the top of the smaller tub should be falling continuously. Tilt the inner tub up at one end (the non holed end) if you need to increase or decrease the water level in the rain chamber.
Problems to fix up: you don't want the precious eggs being sucked through the filter, so superglue or melt some guaze/flyscreen over the holes to stop them being washed outinto the outer chamber.
Clear as mud? Maybe someone else will know what i'm talking about and add to this description. Even an internet search might reveal some rain chamber designs.
Good luck!
-H