I got started on this because I wanted to see if Albert Pujols did it for the last two years. He just missed. More on that later. I set the plate appearance (PA) minimum at 800. The tables below show the winners. Data came from the Baseball Reference Play Index.
What is interesting to me is that in some cases, the winners were far ahead of the other players in all three stats, that Al Rosen was the only guy to do it twice in a row, and that Albert Belle is the only guy to do it since 1954. Rosen was probably only able to do it because Ted Williams was in the Korean War. And Williams is the only other guy to do it twice.
Now back to Pujols. The table below shows the leaders over the 2009-2010 seasons with a 1,000 PA minimum. He's just a bit beind Votto and Ramirez in batting average (BA). I hate it when mere mortals get in the way. May the Gods show them no mercy.
Then I thought "what about a 3-year triple crown for Pujols?" No luck there either, since Ryan Howard beats him out in RBIs. This is the next table. 1500 PA minimum.
Not having the RBI lead is certainly not Pujols' fault. The next two tables show how both he and Howard hit with Men On and with Runners in Scoring Position (RISP). Pujols ends up walking alot more in those cases. In all cases, Pujols walks 13.5% of the time while it is 12.4% for Howard. But with Men On, Pujols' walk rate is about 21% while Howard has 12%. With RISP, those numbers are about 29% & 16%. So, even though Pujols hits alot better with Men On and with RISP, as you can see below, he ended up with fewer RBIs.
But Pujols gets the last laugh. He has won the 10-year triple crown, with a 2,000 PA minimum. This is the last table.