Talk with your university. See if they have a relationship with a program in child life specialist training. This way, you can talk to fellow students and gain a firsthand understanding of the effectiveness of such a program. This represents your best path for finding a reputable internship.
Search online. Look at child life specialist internship postings and review them for effectiveness. Take a look at the roles and responsibilities of the intern. You want to find a program that makes it as hands-on as possible. If you will merely be making photocopies and buying coffee, you should look elsewhere. A paid internship generally brings a higher role of responsibility, so prioritize your search that way.
Apply for internships. Create a resume that showcases your abilities. Even if you have no prior experience in child life, you should include relevant skills that could apply to your roles as an intern. Tailor each resume to the organization to which you will apply. Add in a list of educational and professional references that can attest to your character. Include a cover letter conveying your passion for child life.