Probiotics can improve both the effectiveness and duration of protection of vaccines. A large systematic review (an overview of many different studies) concluded that giving your child probiotics could increase both the effectiveness of the vaccines (usually measured by antibody response) and also the length of protection from the vaccines.
Many different types of probiotics were used in the various studies so it is difficult to give a concrete recommendation, but probiotics containing B. breve, B. lactis, L. acidophilus or L. rhamnosus appeared to be most effective.