There was a Pokemon called Marin, which was designed by a fan. It only appeared in the manga, though.
Marin (Japanese: マリン Marin) is a Pokémon appearing in the Magical Pokémon Journey manga. It appears only on the title page of The Best Gift Ever. According to commentary by Yumi Tsukirino, Marin was designed by a fan in a "draw Pikachu's friend" contest in Japan held by Ciao magazine (Japanese: ちゃお) and first published in the December 1998 issue of the same magazine in which the cover page is presented in color, and Marin's body is shown to be entirely blue.
Another instance of a fan-inspired Pokemon was when someone came up with an idea of a 'possessed' teacup on social media, which they named Polteageist.
Not an inspired design, but some fans speculated that in Ruby/Sapphire the character would be able to fly into space from the Mossdeep Space Centre and catch Deoxys. This was later found out to be false, but in OR/AS you can fly into space with Mega Rayquaza at the end of the Delta Episode and encounter a Deoxys.