A lot of the time fathers played the same general position as their sons. One example is the Kendall family: Jason catches today and his father Fred was a catcher throughout the 1970's. Even when the positions aren't exactly the same, position player dads generally have position player sons (Sandy Alomar, Sr. was an infielder while Sandy, Jr. was a catcher). Similarly, pitcher fathers often have pitcher sons (Mike Bacsik: father, son). This isn't always the case, though. Below I've listed the "crossover" fathers and sons, one a pitcher and one a position player.
Johnny Cooney and Gil Torres both debuted as pitchers before converting to position players, so I included them on the list. I treated George Sisler as a first baseman though he began his career as a pitcher, playing first on days he wasn't starting. Finally, Mel Queen started as an outfielder before converting to pitcher which is why he's on the list. The Meinkes are a debatable inclusion since father Frank split time as a shortstop and pitcher during his only season as a regular.