I had to look to find dates with what I considere as "manageable" connections. You can find this fare very easily using Matrix-ITA, but it often includes extremely long (over 18 hour) connections outbound to JNB and/or very short (less than 1:30) on return to the US. Personally I would be leery of that short a connection at an airport the size of the new IST when you have US secondary security to pass. I haven't connected back to the US on TK via the new IST yet, but it could be a real bottleneck at the old airport.
I found the fare below and was able to reproduce it manually by doing a dummy booking on the TK website for the same dates. I was able to take it all the way to the payment page. It books into fare class J (Business Promotional). This earns at least 20234 award miles on all *A partners, according to WTC (
link).
As per
flyerCO in post #3, this requires booking 2 people.