Newspaper syndicated columnist Robert Bruss championed the idea of rent applied to down payment for the purpose of real estate purchase. He died somewhat unexpectedly in 2007.
He did write a book and you might find one in your library. The title was "The Smart Investor's Guide to Real Estate" (1981)
Here is an article by him about what he termed a "lease option (to buy)." If the property goes up in value while you have the option, you can make some money at this. But, when properties are going up in value rapidly, you won't find many options. this may be a good time to do this, depending on whether you're the buyer or seller.