Yes you can.
Lots of picnic tables available all around except on weekends when they are reservable for birthday parties
They even have a couple of converted old (dining cars ? ) that can be rented out for "in-door parties" on a train. Other than that, picnic spaces around (that can be reserved - for a fee - for group parties on weekends. If you have a group & want to ride around the park on the small train, consider buying a small bunch of tickets & dividing them up with your group. You'll get a much better price /per ticket, rather than buying them individually.
Yes of course numerous picnic tables
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