a diploma in counselling practice can be obtained from the Counselling & Care Centre. However, applicants need to have counselling experience (as a counsellor), and need to undergo an intake interview. Usually, applicants are people who are already in the social services field, esp social workers, counsellors, mediation counsellors, teachers, pastoral care personnel etc.
if you are still young enough, you might want to consider getting a BA majoring in Social Work in NUS. There also seems to be a lot of foreign universities offering distance learning. However, I am not sure if it is accepted in Singapore, in view that counselling requires that special touch. I have no idea how one learns to counsel with the text

You might have to find out from the Singapore Association of Social Workers re: its recognition.
wish you luck!!