Find out the specific brand name the shot (for example, Daptacel or Prevnar) and google it and "package insert" and see if it's in there.
Unfortunately, for many vaccine, they only evaluate the immunogenicity after three doses. And some information is just scattered here and there all over the internet, in obscure scientific studies (you can try searching google scholar, but it'll be an afternoon project, at least) or on the CDC site (like, the fact that one dose of the mumps vaccine is 70% effective is on a page on the CDC site for professionals about the midwest mumps epidemic.)
Sorry!
This site has some of them collected when you click on the diseases on the left, but there's no one go-to source with a comprehensive list of the estimated effectiveness of all the different vaccines that I know of.
