I'm sorry, but I have absolutely no idea about job sites for your line of work – I'm a quantum condensed-matter physicist… there's almost no manufacturing in Singapore, it's too small. However, there is an awful lot of Distribution (mainly freight forwarding) due to the colossal port.
a quick google and Singapore IT jobs or Monster look promising. make sure that you really boast as much as possible on your CV, make yourself look incredible and ensure that you have positively glowing references. this is the Singaporean way – if everything isn't overwhelmingly positive and first class, they're not interested. good luck!