Check out eBay. All sorts of things show up there.
The closest modern equivalent is what they call a "swim skin". Many triathletes buy them for warmer events where a wetsuit either isn't allowed or would just be too warm.
E.T.A.: Wow, those old full body suits seem to be collector's items now! This guy is asking over $1000 for one.
Typing "full body fastskin" into the search function on eBay gets you a lot of older style technical swimsuits. As well as lots of smartphone covers and some truly creepy baby dolls.