I don't know how safe it'd be. Lots of young children running around.
I can't find any information in the city codes and ordinances that says you can't. That being said the park is usually crowded that day and it may be a little too crowded to start up a small BBQ.
There are no approved grills at Pioneer Orchard Park. There are some near the covered area at Sunnyside Beach Park down the road.
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