Полагаю, вы можете решить эту проблему с помощью OnItemSelectedListener.
public void onCreate() {
....
Country[] mCountries = ... ;
final Spinner spinner1 = ...;
final Spinner spinner2 = ...;
spinner1.setAdapter(new ArrayAdapter(mCountries);
spinner1.setOnItemSelectedListener( new OnItemSelectedListener() {
void onItemSelected(AdapterView<?> parent, View view, int position, long id) {
Country country = (Country) parent.getAdapter().getItem(position);
spinner2.setAdapter(new ArrayAdapter(country.getStates());
}
void onNothingSelected(AdapterView<?> parent) {
spinner2.setAdapter(null);
}
});
....
}