If Trump really wants Greenland, he should:
1) Carve out the territory that 95% of Greenlanders currently live in. That is a small strip of southwest coastland from the southern tip, and up about 1/3 of the coast. Call that "Independent Greenland" and they can decide whatever they want. Be a part of Denmark. Be a part of America. Be an independent country. Be a commonwealth similar to Puerto Rico, of EITHER Denmark or America... THEY get to choose.
2) Now, Greenland has a pop. of ~53K, of which ~50K live in this strip of land. Trump could take over the balance of Greenland for "security reasons" (our current military and space bases there...). But he can't just TAKE it. He has to make them "an offer they can't refuse". Think Louisiana Purchase. Or the purchase of Alaska. Just spit-ballin' here: $100 Billion to Denmark. $10 Billion to Independent Greenland? (The purchased portion would be called "State of Greenland" as part of the United States?) 6% royalties for ALL natural resources (at wholesale cost) mined or otherwise, from the State of Greenland for the next 100 years. 4% to Denmark, 2% to Independent Greenland residents? And a promise to develop anything within 10 miles of Independent Greenland (let's say Ports, Shopping Centers, Walmarts, anything) only with their approval. Some distance so they don't feel encroached upon. Also: All residents of "Independent Greenland" have passport/visa-free access to the State of Greenland.
But I'm just Manifest Destiny'ing here...