In paragraph two of the article, Myers uses the popular phrase, "greening of America," but puts quotation marks around it to indicate he's using it in a
new way. What does he mean by it?
What, according to Myers, seems to be the true relationship between
happiness and money? Would Myers say that the relationship is the same
for people living in abject poverty as for people living above the poverty
line? Are the short-term effects of having more money the same as the
long-term effects?

The phrase Greening of America was popularised by Charles Reich when he authored a book by that title which drew loads of accolades as well as criticisms. It rested on several issues.  

The book spoke to the evolution of the American global perspective, using three paradigms which he termed Consciousness.

The first had to do with the self-sufficiency of rural life the next spoke to the New Deal, the second world war and life in the 1950s, whilst the third consciousness he branded "the counterculture’s embrace of personal happiness over material success."  

According to Reich the foundation of the third consciousness comprises of self-liberation from the preprogrammed absorption of society's values.

So when Meyer puts the phrase "Greening of America" in quotation marks Meyer is referring to America's growing sentiments/preference of money as an indication of a better life.  This according to him reflects a cultural   a shift toward greater materialism, money especially instead of self-liberation as already put forward by Reich.

Cheers!