yes
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With breeding 2 normal Pokemon, the chances of getting a shiny Pokemon are 1 in 8,192. By breeding 2 Pokemon from different countries, the chances of the offspring being shiny is 1 in 2028. With a shiny female Pokemon and breeding, the chances of that Pokemon being shiny is 1 in 64. so, yes, it is possible, but it takes forever.
In the second generation, you had a 50% chance of getting a shiny Pokemon this way, but in the 3rd generation onwards, chances were decreased and you did not have a better chance of getting a shiny Pokemon by using this method. Additionally, you won't know if the baby Pokemon will be shiny until it hatches because eggs containing shiny Pokemon do not look any different from eggs that contain non-shiny Pokemon.
if you mean put a shiny magikarp in the day care, yes. however even if you have 2 shiny magikarp it's highly unlikely you'll have a shiny magikarp baby as a result. your chances of hatching an egg and the Pokemon being shiny are the same as your odds of finding a shiny in the wild - slim to none... sorry, Pokemon creators weren't really geneticists the guy who answered this is the same person who asked the question LOL!? i have hatched so many magikarps filling 4boxes or lvl 1 none are shiny so far lol im breeding gyrados lvl 55 with a ditto
It's because Cleffa is a baby form and they're incapable of breeding.
make a baby using a ditto