Google Maps API doesn't support that kind of solution. There are a couple other places from which you can get the coordinates, though:
Flickr API
There is a Flickr API based on photos that people tag, but it's only as accurate as the people who tag photos: so it's good enough for bootstrapping but probably not for production: http://karya-blog.blogspot.com/2012/12/fetching-city-polygons-with-flickr-api.html
Natural Earth Data
An accurate alternative is www.naturalearthdata.com. To get that data from there you just need to make two requests: one with the city name and one with their ID to get the parameters:
unlock.edina.ac.uk/ws/search?name=berlin&gazetteer=naturalearth&format=json
and then
unlock.edina.ac.uk/ws/footprintLookup?format=json&identifier=14126951
and you're set :)
Mapzen
If it's possible for you to pre-fetch the data, go for Mapzen, they have a full and pretty accurate database: https://mapzen.com/data/borders/