Just a little info I dug up. http://hesreport.sunocoinc.com/_filelib/...ar_brochure.pdf
Check out the above link, if you read on the left side of page 1 (Diamond in the rough) and check out the pictures on the right, apparently the arrow and the Sunoco name were added in 1920. So I would think your sign must date some time after that.
Also, on page 2 of the same link is a timeline that states that in 1927 the "Blue Sunoco" name/gasoline was introduced. Now I'm not sure, but I do not believe in my short time in the hobby I have seen the "Sun Oils" & the "Blue Sunoco" used together. If this in any way indicates to us when they stopped using the "Sun Oils" in the diamond logo, then we could possibly say your sign dates between 1920 & 1927. But I do not know when exactly the "Sun Oils" in the diamond logo was last used.
Just a little info. Not sure if it's the whole story. I would love to hear anything anyone can add.
BTW all, check out that pump on page 2. Is that some early blend pump or something?
Edit: After thinking on this a little again this morning, it's likely i'm off on the 1927 part. From what we see in some oil cans, it's somewhat obvious that the "Sun Oils" in the diamond logo is used well into the 30's at least.