Yes, find a trader who will trade you a ditto. Then put in daycare and a few days later.... WALLA you have three or four eevee eggs.
Sources
Happened to my friend he gave lots of eevee. His name was fregley. LOL. :)
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Shinx can breed with an Eevee. I'm not sure what other Pokemon Shinx can breed with.
If you breed an Eevee with a Ditto, then you can evolute the hatchlings into the other forms
Eevee can breed with any Pokemon in the Field Egg Group and including Ditto as well.
Take Eevee to the daycare center with another Pokemon. And make sure that these Pokemon are compatible with each other. Such as Eevee/Ditto, or Eevee/Eevee. You should also try breeding Eevee with other Pokemon to see if there compatible or not. If they 'get along or don't like each other much' you get an egg. If they play with more Pokemon then each other try another Pokemon because you won't be getting another Pokemon.
eevee