If they are your friend *and* shameless, i don't know what you could do? If they weren't your friend, you could tell them you don't want to play anymore. Maybe since they are your friend they don't feel as pressured to hear you when you say the crying is enough?
I would tell them 'look, you are a grown ass man, and if you are going to cry over this game i don't want to be friends with you anymore'.
I (think) drove 2 whiners out of our weekly competitive event. They weren't just people who were upset at bad luck, they were nonstop talkative about how stupid other players at the table were (to their faces) and how they weren't the most threatening deck (and in various situations didn't have the most threatening deck but did have the currently most threatening board state).
I told both of them to cool it because they were coming off rude to other players (especially new ones who aren't as rules savvy and apt at threat assessment at times). They continue. They were whiny, had a victim complex, and were very sore losers and would literally say things like "how do i lose to shitty decks"/"i knew edh was for stupid people but wow" etc. They would whine about how long others' turns were, but then take convoluted turns themselves where they fumbled combos and math and decision trees or tutors. They were just always like this.
A few times i would say something like "don't blow up my stuff, i'm not the one whining constantly", or one time there was a 5+/X doublestrike infect on an open board and i was personally being threatened and i said "but if you attack them, we don't have to sit here and listen to them complain about everything", and it got them killed (and i destroyed their
Grafted Exoskeleton on end step anyway).
Now i can't be too sure, but i do think there is a reasonable chance i got both of them to go away.