Seaching For Customer Service Job In Singapore

Did you already find out who potential employers are in Singapore and contact them? If not do so!
In addition, build your network. You might have to travel to Singapore for some time (not just a month) to do this.

How do i get contacts in Singapore to help me get the job

You need to build a network of people who know you and are in the right position to help you. This is not easy and takes time. I recommend you arrange a visit, for as long a possible but at least a month, to Singapore, during which you visit trade fairs, seminars and other professional events in your industry, talk to as many people as possible and also try to arrange a few interviews already before you leave (e.g. by sending unsolicited job applications to suitable employers and mentioning that you will be in Singapore from xx to yy and would like to discuss with them - since Singaporean employers won't pay for travel to interviews and therefore normally disregard applicants who are outside of the country, this often does the trick).