The "Green" call you tried works fine, I called my first six up with it last year. Open reed hand calls are good and relatively inexpensive. If you want to spend some bucks the foxpro fx5 or the minaska M1 Bandit are good electronic calls and you can use sounds that are nearly impossible to make with a hand call.
Mostly I use open reed calls, red dessert howler, Talley ho, Randy Andersons little dog, however I bought a minaska this fall it's fairly impressive. I think that almost any call will bring them in. Most likely You need to get out away from the pressure, pay attention to the wind and how you set up. Most coyotes within 150 miles of the wasatch front have been educated, except for this years crop of pups.