In Star Tournament, you'll see blue green that are a bit harder to play on. If you win first place, you may use these greens on that same course whenever you want.

Green	How to unlock
Blooper Bay T. Greens	Win Blooper Star Open.
Bowser Badlands T. Greens	Win Bowser Star Championship.
Cheep Cheep Falls T. Greens	Win Cheep Cheep Star Tournament.
Congo Canopy T. Greens	Complete One-On One Putt (All 18).
Lakitu Valley T. Greens	Win Lakitu Star Cup.
Peach's Castle Grounds T. Greens	Win Peach's Star Invitational.
Shifting Sands T. Greens	Win Sands Star Classic.