Q. How do I construct an APA in-text citation and reference when the author and the date are the same?

One citation date would be designated 2010a and the second 2010b.  In-text citation example:  Walker (2010a) indicated that  . . .

The references are alphabetized by title in the Reference List to determine which is "a" and which is "b."  If there is no date, use (n.d.-a), and (n.d.-b).  

For example, this is how you would format these (fake) articles in a reference list:

Smith, A. (2012a). Apples are better than oranges. Journal of Apple Studies, 1(1), 1-10.

Smith, A. (2012b). Some oranges are better than apples. Journal of Citrus Research, 2(3), 20-31.

Then, in-text you would want to make sure to add the lettering onto the dates so your reader knows which source you are citing.

For example:

While Smith (2012a) found that most people prefer apples to oranges, Smith’s (2012b) follow up study found that some oranges are typically preferred to apples.

For more information, see pg. 305 of the 7th Edition APA Style Guide.