If you're talking about the weekend of May 4-5, the closest game to Taipei might actually be the Sunday one between the President Lions and Lamigo Monkeys in Douliu. However, there is a lot more to see and do in Tainan, so the Saturday game would probably make for the more interesting trip.
However, you mentioned wanting to see Manny Ramirez. The team Ramirez is with, the EDA Rhinos, are playing the Brother Elephants at the Chengching Lake Stadium in Kaohsiung on the 4th and 5th (both games starting at 5:05 p.m.), so I would think you would want to go to Kaohsiung rather than Tainan next weekend.
I know the presence of Ramirez has created a buzz in Taiwan, but in general CPBL games are rarely sold out (the numerous game-fixing/gambling scandals over the years have seriously affected attendance), and you should be able to buy a ticket at the stadium on the day of the game. My Taiwan-born wife has assured me, however, that you can also buy tickets online and at convenience stores, just as in Japan. The owners of the President Lions, the Uni-President Corporation, also operates 7-Eleven in Taiwan, so you can probably buy Lions tickets from any of their branches (and 7-Elevens, as you no doubt know, are everywhere in Taiwan!).