Birthday in a Park for a 2 Yr. Old

Even 2 year olds like a pinata. Just fill it more with little toys (no small detachable parts) than candy. Healthy snacks - cut up fruit is always a hit.
little sandwiches cut in triangles/no crusts, cut up vegetables, maybe with ranch dressing.

what ages of children will be attending? bubbles are usually a big hit with small children, and beach balls of various sizes are good b/c they don't move fast enough to cause 'owies' ;-).

Food: pizza is good (you might even be able to get it delivered
chips (soft cheetos may be best esp for little kids)
peanut butter filled celery (check for allergies first)
bottles of water
little boxes of juice

Depeding upon when you're having it & the weather- Games:
water balloon toss
bean bag toss
pumpkin decorating contest
face painting

You don't really need to decorate but you could:
get a few helium balloons to tie to the table
a cute theme oriented table cloth
a poster board sign decorated w/big markers & sickers (on an easel you bring from home)
streamers hung from tree limbs (if the park lets you. You could even have them affixed to a long rope or string ahead of time so you can just put it up)

I've been to a couple little kid b-days and the pinatas are always a big hit! I know your son is only 2 but, if there are older kids, this would be fun. I just went to a 1 year old b-day where they had one.
At the same party, they had a pirate theme and had little arms bands and face paint for the kids. They had little plastic buckets for Halloween for the kids to collect their candy. You could always do prizes, graham crackers, and goldfish in little packets or something a little less sugary.
I wouldn't plan too many games. Maybe bring a couple balls for the kids to kid around.

We did pinwheels with a strawberry theme. We Served cupcakes and make your own sandwiches with chips and dip and fruit salad. It was easy and awesome. We didn't really need games but we brought duck food and buckets and shovels. You can use the pinwheels for favors too.

You know what my first thought/picture was in my mind when I read your post heading? How many different directions can 2 year olds run. I can't imagine anything less pleasant. I hope you guys have a wonderful time int he park.

I would say all finger food, tippy cup drinks, lots of wipes, and lots of things to keep them busy.

S., Pick a theme and have fun with that. With 2y/o they get over whelmed easy so do simple things. Consider will there be mostly young children or is it family and friends of all ages coming? At the park with all that is going on you don't have to plan much for sure. Since I don't know what time of yr. this is for make an alternate place becasueof weather. Children's finger fods like vegetables and dips, yougarts and juice as well as jelly sandwhiches. You will have some children with specail diets but I have learned that when invited out the parents will plan for the childs needs so ask the family to have something or let them handle it.

We had my daughter's first birthday in a local park and it was a blast. I decorated the ramada with balloons and a big birthday banner (that blew down), had some little hanging decorations that I hung from the rafters and that was it for decorations. I didn't do any games, since the kids were a wide variety of ages (0-6), but they entertained themselves on the playground the entire time. We had it in the middle of the day, after lunch but before dinner, so we served Mexican mini-appetizers, chips, salsa and guacamole. Cake too, of course! I had water bottles for the kids and beer for the grown-ups. It was easy, simple, not a lot of trouble and everyone enjoyed themselves. Good luck!