How can a coach help with chances of being admitted to an Ivy league?

If there are no sporting scholarships offered at Ivy league colleges, how can a coach improve the chances of a potential student-athlete?

As a student-athlete, you are view differently. Your skill makes you stand out, and if you can match or get close to regular students on the grounds of academics, then you have a huge advantage. To them, this shows you can manage your time efficiently to succeed in your sport and in academics which is what Ivy League schools look for. It is about success in all areas and not just in the field of academics. The coach can convince the admissions to accept you even if your academics may not be as convincing as a regular student. They usually note you down, so admission officers know who is an incoming student-athlete. Also, the top schools cherish athlete prowess as this is a big culture in college athletics. It is about expanding the school in all areas, not just academics.