Can anyone recommend a few good picnick-y dishes for an outdoor first bday party with 50+ guests? thanks!

How about pesto pasta or a super simple edamame bean salad (edamame beans, corn--you can use frozen, and cherry tomatoes). A wheatberry salad, of which there are a few on this site, or a curried Israeli couscous salad might also be nice. Going in a different direction, I am also a sucker for a good peanut butter and jelly sandwich. If you can get some great strawberry or cherry jam, fresh peanut or cashew butter, and good whole grain bread, go for it. Cut into fours, there's nothing better. That said, on 3 dollars a person good jam and PB might also be hard. BUt definitely easier than chicken, meat, or fish.

While certainly not in the 'foodie' catagory. Hot Dogs, Baked Beans, coleslaw are good cheap combo for the budget. A small crock pot can keep the beans warm an amazingly long time without power (which I wouldn't suggest with kids running around and extension cords). Chafing dishes would be safe for the beans and hot dogs warmed with sterno--which is pretty safe with large stable chafing dishes just be sure no table decoration can get to the flame, slaw in a chafing dish with an ice water bath can keep outside, Or the pasta salads, and green salads. You can switch out the baked beans for corn on the cob as another option: cutting the corn in thirds or half before boiling and serving for small hands or appitites. Or switch out the hot dogs for some of the meatball recipes here (a bit labor intensive tho).

Thank you all for the wonderful suggestions!! We're going with a partial potluck, and luckily (should I say "unfortunately"?) a few people can't make it so now we're down to 35. Phew. Thanks again, everyone! (Bugbitten, I love your suggestion about the birthday candles--what a sweet idea.)

Pot luck it! So much fun and you wind up with a great variety of dishes. What's more, people usually make their specialty, which is often a good thing.

Cook some quinoa. Add one inch pieces of green bean and chopped walnuts. Season with salt, pepper, olive oil, and balsamic vinegar. Proportions don't matter- do to taste. Can sit out.

You can leave most anything out as long as there's no mayonnaise in it! That can cause real problems. However, vinaigrette dressings are delicious on pasta and potato salads, and you can avoid potential food poisoning.

I also echo the sentiment to go "pot luck" rather than to limit yourself to a $3 per person budget. That's a pretty spartan amount if you want to serve any meat at all.

How many of the crowd are going to be babies too? Or is this a party for doting friends and relatives? Also bear in mind the time of day - if it's a mid afternoon do, then people should have already eaten lunch, and shouldn't be expecting/wanting a full on meal-stuff to snack on and cake should be enough.
How about some cute hand pies? Cornish pasties, empanadas or something? You can make them well in advance, they're easy to serve, easy to eat, pastry is cheap to make, and you won't need much filling in each one. If you've got a tiny "1" shaped cutter, or some other pretty cutters, you can identify different flavours quickly and easily with a different shape on each sort (I'm guessing you'll need one meat flavour and one veggie? You could make others depending on how much time you want to spend on it)

I'm going to duck your question for a moment and suggest that you serve everyone a cupcake with one lighted candle, and have the whole group blow them out in the same moment. Whatever you've served before that won't matter much.

Penne salad with chicken, leafy salad with green goddess, crunchy bread.

p.s.
Here's Oprah's listing for the Chicken Marbella recipe:
http://www.oprah.com/food/Chicken-Marbella

Agree with Benny's point: $3 a plate is not a lot. Does that include beverages, condiments, paper plates, napkins, cutlery? Perhaps some of those 50 attendees could bring pot-luck dishes too? Often people love bringing their "favorite" dishes for others to enjoy - you might need to guide them a bit so you don't wind up with 20 kinds of hummus.
The original Silver Palate cookbook's Chicken Marbella is a famous, reliable party dish, good at any temperature - cold, room temp or hot. Inexpensive if made with chicken thighs and you buy the olives & dried fruit in bulk at a discount store.
This is the cookbook: http://amzn.to/JXCObL. Your library probably has the cookbook and the recipe is also online (although some of the online versions of the recipe are poorly transcribed - i.e., mistakes.)
In any case... have a great party!

I would do something like a whole grain salad (farro or quinoa) in a vinaigrette and herb type dressing, with lots of crunchy veggies chopped up in it. No dairy so you don't have to worry so much if it sits out for awhile. And inexpensive!!

at $3 a plate?? does that include the cupcakes? I would shoot for mini sandwiches. You can do an assortment and cut them up into smaller portions.