You can't find one but you can try to hatch one (which is extremely difficult but possible). All you need is a slugma or macargo to make eggs hatch faster (not required but highly recommended), a male pikachu and a female pikachu or ditto with any pikachu, and if you want, give your female pikachu a light ball (obtained by catching a pikachu in the safari, which has a 5% chance of having one) and breed it with a male pikachu to make the pichu's you hatch have volt tackle.
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The shiny stone is not obtainable in emerald. It was only made in gen 4 (I V)
no
you keep catching pichu until you get one or you use action replay
yes. its a 1/8000 chance you will find one.
Breed a female pikachu that is holding a light ball, and a ditto at the daycare center. Then if you are really lucky, a shiny pichu with volt tackle will hatch out of the egg.