The @FacesConverter isn't an eligible injection target. Replace it by @ManagedBean or @Named. As you'd like to use CDI as as well, use @Named.
@Named
@ApplicationScoped // I assume that your converter doesn't have any state.
public class MyConverter implements Converter {
// ...
}
You only need to change the way it's been referenced in the views. You cannot rely on forClass anymore. You'd need to explicitly specify it as #{myConverter}.
<h:inputSomething ... converter="#{myConverter}" />
or
<h:inputSomething ...>
<f:converter binding="#{myConverter}" />
</h:inputSomething>
If you really need to keep the @FacesConverter in favor of forClass, then you'd need to grab the EJB manually by JNDI. A concrete example is shown in this blog article. I can however not tell that for CDI beans.
The JSF guys have confirmed this embarrassing oversight and they will make the @FacesConverter an eligible injection target in upcoming JSF 2.2, see also JSF spec issue 763 JSF 2.3.
See also:
Update if you happen to use JSF utility library OmniFaces, or are open to using it, since its version 1.6, when just having OmniFaces JAR in /WEB-INF/lib, all @FacesConverters (and @FacesValidators) in your webapp automatically become eligible for CDI and EJB injection without any extra effort.