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.