You can find more about the European situation at the link below, don't know about the other continents: http://ec.europa.eu/eurostat/statistics-explained/index.php/Urban_Europe_-_statistics_on_cities,_towns_and_suburbs_-_green_cities

Venus,

As Mihai has said, there probably good data sets available for European countries, but coverage in other continents will likely be patchy.  There is a second problem in using data from several sources - you cannot be sure of the sampling techniques applied whether they are compatible or highly variable.

Can I suggest a different approach?  Collect your own data using Google Earth Maps and the most up-to-date Times Atlas with a comprehensive list of cities and population.  Using a sheet of paper, lay the edge across a transect of any chosen city and mark in both ends of your transecting, then mark in all green space lying along the transect.  Do the same procedure in random directions across he same city.  Once done, measure the segment lengths of green space, add them together and work out the percentage green space relative to built-up area in all transects.  Using this method there is no need for unit measurement as you will have a ratio that you can then use with the city population data.  The beauty of this method is that the same sampling technique is applied throughout and you results will then be 100% comparable.   Judging where individual city boundaries start and finish is problematic, but if you can get city areal size you could apply that instead.

The method is simple and not necessarily time-consuming, but it does provide first hand data.  Hope that this helps.

Regards

George

The USDA has an Urban Tree Canopy database: 

https://www.nrs.fs.fed.us/urban/utc/

That would be a measure.  They might well also have parks and green space measurements.