There is no on-line search facilities for BMD research on Singapore. There are also no researchers that I know of based in Singapore.
The Singapore Archives (which one would have to visit - no online BMD search facility,except for their search site www.a2o.com.sg ) has most of the records, but certain records need access permission from the "owner", that is the Church. The closest online on Singapore would be the IGI online search of the Latter Day Saints (LDS); but this is very limited. The India Office (London) records of early Singapore would be the best bet, but not online - you have to go there. For India Office and later Church records, the LDS also have microfilmed the Church (Anglican and RC) records which cover an extensive number of years. Get to them online and check on your closest Family History Centre.