Admittedly, the monosyllabic character of every word in "kill two birds with one stone" is convenient, and so at least that aspect of it should be preserved in any candidate replacement. Obviously then "complete two tasks with one action" does not fit the bill (pun intended).
How about "feed two bats with one fruit"? Or - if we wish to redeem ourselves for past abuses - "feed two birds with one bug seed"? Although these may sound strange at the moment because we are so used to the violent alternative, I think they are good candidates.
What do you think? And do you have any suggestions of your own?