The most recent episode of the JFN radio show Ikimono-gakari's garden party (いきものがかりのgarden★party) mentioned that a special Eievui that knows the move Sing will be released to tie into Ikimono-gakari's vocalist Kiyoe Yoshioka's role in the upcoming movie short Pikachu and its Eievui Friends. Further details on the Pokémon and the distribution will be revealed via the official site at a later date.

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Source: いきものがかりのgarden★[email protected] via http://park3.wakwak.com/~pokepale/

Official Site Update - June 15th, 2013

The official Japanese website has updated and announced the full details of this event. To celebrate the debut of the 16th movie in theaters on July 13th, 2013, a special event will be held at LaLaport TOYOSU. Shoko Nakagawa will be in attendance as will Ikimono-gakari (いきものがかり) who will perform the song Egao (笑顔). Those that wish to attend the event must sign-up for the lottery on the official movie website. Spaces are limited and will be chosen via lottery. The Eevee will be distributed to those that attend the event.

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For those that cannot attend the July 13th event, those that purchase the Egao (Limited Edition) CD which goes on sale July 10th, 2013 will receive a voucher that can be exchanged at participating Toys 'R US locations and Pokémon Centers for the Sing Eevee. The promotion will be from July 14th, 2013 until September 1st, 2013.

Pokémon Info
pic Level: 50
OT: Kiyo (キヨ)
Held Item: Silk Scarf
Ability: Adaptability
ID: 07133
Move 1: Sing
Move 2: Return
Move 3: Echoed Voice
Move 4: Attract

Sources: http://www.pokemon-movie.jp/topics/event_lalaport.php and http://www.pokemon.co.jp/info/2013/06/130615_m01.html