Dinosaurs most likely had a Syrinx, just like their bird descendants. And a syrinx is much more capable of making a wide variety of noises (and it generally does not involve the hyoid bones) than the mammal larynx.

As for modern birds "chirping". Modern birds have a very wide variety of sounds they can make. Take an ostrich for example and google what kind of sounds they can make (make sure to google ostrich mating call since many results don't bring that up).

Or google lyre birds if you really want to know the capabilities of a birds syrinx when it comes to generating sounds.