How can I patch a leak in my sprinkler system manifold?
There are epoxy-based putties designed for leaks like this, but your sprinklers might work at a pressure higher than the putty can handle.  JBWeld makes one which is sold in home improvement stores.

If you try it, be sure to leave the water off while the putty dries, and use enough to circle the entire leaky joint.

Wear gloves to mix and apply.  Don't expect to be able to remove the putty from anything it is attached to - when you replace the manifold you'll need to replace the puttied parts too.