Answer:
I think the second one: I am eager to be a part of the Summer in the Park program.
Explanation
This choice uses strong, formal language like "eager." You want to be formal because you are applying for a job, even if it is just working at the park. Also it directly states what you are applying for. "Summer in the Park program."
"I think working in the park would be a cool way to spend the summer." This uses words like "cool," which aren't very formal. It also doesn't sound very sure and professional, since it starts with "I think, " instead of something strong like "I believe."
"Hanging out with little kids in the playground would be a hoot!" This uses slang and doesn't sound as professional.
"All that fresh air plus some cash sounds like a winning combo to me!" DEFINITELY not this one, as it uses slang again, but also talks about doing it for the money, and I'm sure your boss might think that makes you sound like an irresponsible teen! oof
