Could one country just buy another instead of taking it by force?

Researching an earlier question, I came across this article in which the US is supposed to have offered to buy Greenland from Denmark.
Could this happen today? I realize that there are few countries owned by other countries at this point but who would you contact about purchasing another country you were interested in? Would it be cheaper than going to war? How would the sales price be split? Would the population benefit from the proceeds or only those in government? Could you have a vote and majority oks the sale then it goes through?
With the Global Corporate Takeover of the world is this something we may encounter in the future?

If it were an option, what country would you like your present country to purchase (be realistic, Norway could not purchase Russia but might be able to get a good deal on Finland or Monaco but Russia could probably afford Norway).