Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear that your pup ate something he should not have.
Natural leather baseball covers are absorbent and can expand in the juices of the gastrointestinal system. If he chewed it up quite a bit into small pieces first, and because he is a big fellow, it may pass. But if he just ate it, within the past 2-3 hours, it's worth trying to get him to vomit it back up, especially if it is plastic not leather.
You can give him 1 tablespoon of 3% hydrogen peroxide per 10 pounds of body weight mixed with bread chunks, dry dog food, or ice cream (no more than 3 tablespoons of peroxide at a time even though he weighs more than 35 pounds).
Then take him outside and run him around to get the peroxide bubbling so he vomits.
If no vomiting in 10 minutes repeat the peroxide dose once.
If he vomits and seems to clear his stomach and be done I would check to see if the pieces are present.
Once he finishes vomiting and empties his stomach to try and settle his stomach today you can give either:
1) Pepcid-ac (famotidine) at a dose of one 10mg tablet per 20 to 40 pounds of body weight every 12 hours. (2 tabs for a pup his size)
2) Prilosec (omeprazole) at a dose of one 20mg tablet per 40 to 80 pounds of body weight every 24 hours.
These will reduce stomach acid and should help settle his stomach and decrease the irritation from the peroxide.
Then feed a homemade diet of 1/3 boiled, lean hamburger or boiled, white, skinless chicken, all fats and juices drained off the meat, and 2/3 boiled, plain, white rice. Add 2-4 tablespoons of canned pumpkin, (not pie filling, just pumpkin), to each meal for fiber whether he vomits most of the foreign material back up or not to help push any remaining pieces through.
If you don't have peroxide you can get him to an emergency clinic to induce vomiting if you choose to.
If he doesn't vomit it back up or you choose not to take him to an emergency clinic but rather want to see if he can pass it still use the bland diet with pumpkin to try and get the pieces to pass.
If it has been several hours since he ate the ball cover it is likely too late to induce vomiting, the pieces will likely be out of his stomach. All you can do at that point is watch him closely. If he starts vomiting, has a tense painful belly or refuses to eat or runs a fever (more than 103F rectally) then that can signify a blockage and he should be seen by a veterinarian immediately. Surgery may be needed at that point.
Please let me know if you have any further questions.