해당 어플이 시스템 권한을 가진 시스템 어플리케이션이라면
String target = "com.google.android.marvin.talkback/com.google.android.marvin.talkback.TalkBackService"
Settings.Secure.putString(getContentResolver(),
Settings.Secure.ENABLED_ACCESSIBILITY_SERVICES, target);
Settings.Secure.putString(getContentResolver(),
Settings.Secure.ACCESSIBILITY_ENABLED, "1");
<uses-permission android:name="android.permission.WRITE_SETTINGS" />
<uses-permission android:name="android.permission.WRITE_SECURE_SETTINGS" />
이렇게 설정 가능합니다.