Q. For APA style, how do I cite an electronic source date when it gives a span of dates like (2009-2014)?

I am going to assume when you say "electronic" you mean a webpage? Usually a website will do that type of blanket coverage of dates like you mention in your question, "2009-2014."

I have never seen APA address this issue, so ...

a). Double check the page you are citing to see if there is any mention of  a creation date.

b). If not, then at the bottom of the page use the copyright date range, i.e. 2009-2014. I would use the most current, single year - 2014.

I usually like to answer questions with a definitive chapter & verse from the APA manual. If your professor does not approve of my interpretation then they must know the right way and can share ...  ;)