Yes most plastic reed type cow calls seem to saliva up, especially when needed the most. The cow call you describe is called the " Sceery" or something like that. (spelling) Another of my favorite ones is called the " Hyper Lip Single" by primos.
In addition to one of those or both, is a mouth diapghram reed in your mouth, like a single or no bigger than a double reed, you can make great cow sounds with these as well, they all complement each other. elknut1