Do you need the rats to survive for a longer period? If not overdosing with pentobarbital and removal of salivary glands should probably do the trick. Mandibular salivary glands are located just under the skin. A midline incision on the neck with a rat in supine position will expose these glands (they are fairly big). You can try collecting them and extract saliva from the source.
How much saliva is needed ?. You use small dropper. You pour little distilled water in oral cavity and you can re-suck with same dropper. You have to repeat it for longer period.