Crier is the preferred spelling of the noun referring to (1) one who cries, and (2) a person who makes announcements in public places. This is the case in all modern varieties of English. You might see cryer in old books,1 but this spelling was always less common than crier and has gradually disappeared from the language.2
Similar word pairs have not followed the same trajectory. Both drier and dryer, for instance, have stayed in the language and now have different meanings, while flier and flyer are both common and are mostly interchangeable.
It usually starts at Marshfield Market Place at 11am, with the mummers being led through the streets by the town crier. [Financial Times]
[He] mentioned that it can be uncomfortable to sit next to a client who is a crier. [New York Times]
But an interesting change of approach as world class crier Kate swapped cascading tears for theatrical breathlessness. [Mirror]
Nice guy Goreski, who became known as kind of a crier during his prior second-banana gig on The Rachel Zoe Project, remains unashamed about the weeping. [National Post]