What solutions have the world's leader suggest for slowing the growth of world population?

The "solution" to overpopulation would essentially be getting the crude Birth Rate to equal (or become lesser) than the crude Death Rate. As such, the natural increase rate would reach what's called zero population growth (ZPG). The question you're asking is how do we reach ZPG?

Well there are two ways: Increase the death rates, or lower the birth rates.

Few people wish to see the former applied, leaving the latter as the only alternative. This is where the debate is - what is the best way to reduce birth rates? One alternative emphasizes reliance on economic development and the other on distribution of contraceptives.

1) Economic Development Alternative

A wealthier community has more money to spend on educaton and health-care programs that would lower birth rates. According to this method, women who receive more education stay in school longer, are more likely to learn employment skills, and gain more economic control over their lives. With better education, women would make more informed decisions regarding their reproductive choices and selecting contraceptives.

2) Distribution of Contraceptives

In the long run (and over a huge amount of time), economic development would promote lower birth rates (look at the evolution of the U.S. from the 1700s to modern day and compare with birth rates) but the world does not have this much time. Allocating resources in family-planning programs could reduce birth rates rapidly (look at Colombia, Morocco, and Thailand for evidence). Another example would be Bangladesh, which has seen little improvement in their economy, but with the increase of contraceptive use, their birth rate has in fact declined.

But again there are problems that arise from this "solution". Many groups of people oppose contraceptive and birth-control programs for religious and political reasons.