Things that have worked for me so far:
-Deep breaths after a death. Take the time to respawn as a breather, take a drink if one's nearby, etc.
-If you're being flamed, remember that the person crapping on you doesn't know what YOU see as a player, or if you've misclicked or just had a bad moment.
-If someone else is being flamed, try your best to remain optimistic about the fact that the flamer is so wrapped up in other people's play they may not be critical of their own mistakes. (That being said, don't call them out on it in chat, it might not go over well for anyone)
-Remember Lux and her RIDICULOUS optimism. (We can do this! We're in this together! DEMACIAAAAA!)
-Try and pick champs with funny banter/lines (Lulu's nonsense is particularly good for cheering me up, as are Nami's criticisms of feet.)
Stay positive! You're doing the right thing by trying to avoid tilt, and that's commendable in itself [slayer-jinx-catface]