to the OP: if you want to start a poll, you should define the terms and establish a concept of evaluating coaches.
greatest running coach? what makes a coach great? what is great? what is running (sprinting vs. distance vs. hurdles or all 3)? Are we talking development--high school to college to international?
Is the evaluation based upon most olympic medals? world records? world records/ medals in comparison to the given country's population?
I'd say Lydiard is the most influential. He did a great job working with athletes and has had a tremendous influence on distance running around the world. Greatest coach? considering that his athletes posted times that would still be considered world class, in a country the size of California with the population of San Francisco, then yes, I'd say Lydiard is probably the best.
Bowerman? I'd say greatest Track & Field coach of all time, but not necessarily "running." He had a great understanding of all events, and was passionate about each one, not just one grouping of events.
I think honorable mention should go to Mihaly Igloi, who did a tremendous amount working within a small framework.
Honestly, I really don't know of more international coaches outside of Canova and Lydiard. Canova seems to be doing a great job with his athletes--but did he develop them like Lydiard did, or were they already good when they came to him?