The Godfather Suite does have recordings of the songs in Connie's Wedding--"The Godfather Tarantella" (Clemenza dancing), "The Godfather Mazurka" (Sal and little girl), and the "Godfather Fox Trot" (Connie and Carlo dancing). Tracks 2, 3, and 7 respectively. However they are different recordings than the ones in the film, the orchestra is beefed up considerably. Good recordings, but for me, it doesn't have the same feel as what was actually used in the film. You can hear 30 second clips off of amazon.com:

http://www.amazon.com/gp/product/B0.../0 02-7216771-0048840?%5Fencoding=UTF8

As for the Manhattan Serenade (California), the only recording I've been able to find is on the CD "Mob Hits 2". And it's again different from the Godfather film and has female vocals. The quality is also not the best on that CD.
And finally, I've never, NEVER, been able to find a recording of the song that plays in Vegas, I wish I could.

Hope this helps!