I umpire a lot of softball, so I use the ASA lineup card holder, even when I umpire baseball.
Each side has a clear plastic sleeve that extends halfway across the side in order to tuck the lineup cards into. But I've found that to be more of a pain than it's worth because when I slide the card out to make a change, sometimes I have problems trying to slide it back in.
So I just use two small metal binder clips
one on each side, to hold the cards down. And I keep the holder in my ball bag so that I don't have to worry about them getting wet from my sweat on those hot days. I've never had any issues.
Of course, the vast majority of the baseball that I do are in organizations that don't ask umpires to keep cards. In the off chance I do, one of my ASA holders has the logo covered so I don't get some coach think, "Aww, geez, he's a softball umpire..."