You are correct, they are short but only typed pilots are being hired.
For the 737 series, you have 3 options. Jet airways, Jet Lite(formerly sahara) and Spicejet. The comment about jet having enough captains is also true for the 737's. Though you can talk to them and see what they say.
spicejet would be the best bet i think. They are getting 3-5 new a/c over the next 6 months and therefore the requirement. Age is no prob, upto 65 is ok