It is true that there are opportunities for teachers of Tamil in countries like Singapore and Malaysia. However, at present the chances are fewer. Those who have excellent skills and academic qualification get good opportunities. Nevertheless, you must register your qualification and experience at Overseas Manpower Corporation Agencies at Chennai run by the Government of Tamilnadu. The charges collected is quite less. Only after registering with this agency, recommendation letters are given by getting particulars of the organization to which you have applied.
For details:
E-mail:omc@md4.vsnl.net.in
Web-www.omcmanpower.com