How do I make a map have a rain?

Weather has never been fully implemented, only experimented with so don't expect a perfect result. That said you can get an alright rain effect by following this (it's a little technical):

1. All the level objects you see in the screenshots need to be copied from Jungle Rock Island over to the level you want to add rain to (JRI was set up a while ago as a quick test), the fastest way to do this is to use a text editor and copy them from the .json in JRI and paste to the new map but this might be difficult so you could also just make a new object and manually enter the values from the screenshots (you only need to make 2 rain objects and one audio object)
2. Drops - set numDrops to 200 in both "rain_single_drops" and "rain_coverage", you should see rain fall now (if there's no splashes you might need to disable and then enable the doCollisions checkbox)
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3. Rain sound - set "sourceGroup" to AudioChannelEffects, track to amb_rain_medium
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4. Sky colour - in the paths for the four gradient images swap "default" to "overcast" and change the time to update (you can use the ingame time of day)
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5. The overcast sunScale gradient is a bit too bright so you could choose a dark grey for the sunScale colour/edit the gradient (this will be lost if you change time of day though)
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I hope this helps.

 

A mod for the map would probably be the best way to do that.