Try this...
When they rage at you, and flame in chat... Respond by saying "fuzzy kitten."
If they persist, say "sweet bananas."
Should their crying rage fest go forward from this point respond with "sweet kitten."
If none of this has helped the situation, and they continue to moan try "fuzzy bananas."
This will do one of two things. The feelings of fuzzy kittens and sweet bananas will calm them, or they will realize you arent giving them the satisfaction of acknowledging their impotent rage. Now the second reaction will make them even angrier for a bit, but then they will burn out on rage, forget, and reset like a baby that saw a face it recognized or got its bottle back or something.
The most curative and calming thing for the typical crying ADC syndrome is just moving on like you dont even care. Sure, they will cry, but once they realize no one gives a fuck, just like a baby... they will eventually stop crying.
Now me... I know if this is the attitude, or behavior of my ADC... Im expecting a loss anyway, so I lay into their fragile ego: "(takes one CS, rage starts) Oh... my bad... but if that one minion was the difference between winning and losing this lane, we were fucked anyway... may as well take more now...." Then just mute them. What will happen is they will cry and cry and cry. Then report them for verbal at the end, and eventually they will get chat banned and learn to stop typing a salty rage novel every match cause support took a couple minions.
Good luck.