Match coins game

[snippsat]

Change method set_amount,then it should work:

def set_amount (self, value):
    self.__amount += value

The  getters/setters and __(which is not private),could be removed.
Double underscores __ is used for name mangling,nothing is really private in Python.
Not your fault but your teacher who comes from a Java/C++ background,
and do it in a same as those languages in Python.
So could look like this:

import random

class Coin:
    def __init__ (self, amount=20, sideup="Heads"):
        self.sideup = sideup
        self.amount = amount

    def toss(self):
        val = random.randint(0,1)
        if val == 0:
            self.sideup = "Heads"
        else:
            self.sideup = "Tails"

c1 = Coin()
c2 = Coin()
play = input('Do you want to play? (Y/N): ')
while play.lower() == 'y':
    c1.toss()
    c2.toss()
    if c1.sideup == c2.sideup:
        c1.amount += 5
        c2.amount -= 5
        print("player 1 wins")
    else:
         c1.amount -= 5
         c2.amount += 5
         print("player 2 wins")
    print(f'player1: {c1.amount} and player2: {c2.amount}')
    play = input("Do you want to play? (y/n): ")