Baseball Players Autographs

I've brought my 3 young kids to around 6 games lately with their attempt to get all autographs on their baseballs (and my little girl wants her hat signed), and the 1st base line and outside gate 2 only produced Tommy White once and the rest of the players are our "supporting role" players, and not the top players like Skenes, Crews, Floyd, Thompson, Dugas, etc. If there is a new location or way to get their baseballs completed, please let me know. They are just now getting excited about baseball, to my surprise, and I don't want them to lose that passion. Please mail me at jrhebert76@gmail.com (<- changed my email, other one wasn't working) with any tips.