Looking at the way the stadium is split up for Orix games (http://www.kyoceradome-osaka.jp/ticket/buffaloes/), the seats with lower child prices tend to be the open seating areas in the outfield and off to the side. They’re probably your best bet.
The last game I went to was at Jingu Stadium in Tokyo on a weeknight. Stadium layout was similar: the hardcore fans were in their designated sections and the casual fans who filtered in after work tended to go to the open areas where we were. I bet the crowds would be different on a weekend, though.