The map on the website for Nankai Namba Station indicates both coin lockers and a 手荷物預かり所, which normally means a counter with a person behind it.

Since Nankai Namba has an express train to KIX and is connected through tunnels to the Midosuji Subway Line (and possibly to JR Namba as well--I don't recall), that might be the best place to store your bags.