MLA
Include the authors' first initials with the parenthetical citation: (S. Rogers) vs (B. Rogers).
On the off chance their first initials are the same, write out the first name in the parenthetical citation: (Steve Rogers) vs (Sam Rogers).
APA
Even with different years of publication, we'll still add a first initial to distinguish the authors: (S. Rogers, 2009) vs (B. Rogers, 2014).
If they have the same first initial, then (like MLA) you'll write their whole first name: (Steve Rogers, 2009) vs (Sam Rogers, 2007) AND you'll note the first name on the references page, since normally only the first initial would appear there.
Rogers, S. [Sam]. (2007). This is an article title stand-in...
Rogers, S. [Steve]. (2009). This is another article title stand-in...
Chicago (CMOS)
Not an issue -- thanks, footnotes!