Adding a particle effect to my clicker game

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See How to make image stay on screen in pygame?.

Use pygame.time.get_ticks() to return the number of milliseconds since pygame.init() was called. When the coin is clicked, calculate the point in time after that the text image has to be removed. Add random coordinates and the time to the head of a list:

current_time = pygame.time.get_ticks()
for event in pygame.event.get():
    # [...]

    if event.type == pygame.MOUSEBUTTONDOWN:
       if coin_rect.collidepoint(event.pos):
           pos = ... # random position
           end_time = current_time + 1000 # 1000 milliseconds == 1 scond
           text_pos_and_time.insert(0, (pos, end_time))

Draw the text(s) in the main application loop. Remove the text when the time has expired from the tail of the list:

for i in range(len(text_pos_and_time)):
   pos, text_end_time = text_pos_and_time[i] 
   if text_end_time > current_time:
       window.blit(text, text.get_rect(center = pos))
   else:
       del text_pos_and_time[i:]
       break

Minimal example:

import pygame
import random

pygame.init()
window = pygame.display.set_mode((400, 400))
font = pygame.font.SysFont(None, 40)
clock = pygame.time.Clock()

coin = pygame.Surface((160, 160), pygame.SRCALPHA)
pygame.draw.circle(coin, (255, 255, 0), (80, 80), 80, 10)
pygame.draw.circle(coin, (128, 128, 0), (80, 80), 75)
cointext = pygame.font.SysFont(None, 80).render("10", True, (255, 255, 0))
coin.blit(cointext, cointext.get_rect(center = coin.get_rect().center))
coin_rect = coin.get_rect(center = window.get_rect().center)

text = font.render("+10", True, (0, 255, 0))
text_pos_and_time = []

run = True
while run:
    clock.tick(60)
    current_time = pygame.time.get_ticks()
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False
        if event.type == pygame.MOUSEBUTTONDOWN:
            if coin_rect.collidepoint(event.pos):
                pos = pygame.math.Vector2(coin_rect.center) + pygame.math.Vector2(105, 0).rotate(random.randrange(360))
                text_pos_and_time.insert(0, ((round(pos.x), round(pos.y)), current_time + 1000))

    window.fill(0)    
    window.blit(coin, coin_rect)
    for i in range(len(text_pos_and_time)):
        pos, text_end_time = text_pos_and_time[i] 
        if text_end_time > current_time:
            window.blit(text, text.get_rect(center = pos))
        else:
            del text_pos_and_time[i:]
            break
    pygame.display.flip()

pygame.quit()
exit()

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