The Hero's Portion in modern era
I think the basic premise would be a great addition to the festivities around one of our rituals, but it would have to be put in context for our current lives. It just wouldn't be practical to go tearing through Madison county in a chariot race, even if it does sound like a lot of fun. Plus our society is a lot more egalitarian than that potrayed in the old tales. While stone throwing may sound "traditional", it is about as fair as having a knitting competition. So the challenge would be to have a series of contests that would be balanced overall and doable in an hour or so.
Horseshoes. Doesn't rely on strength, and even though horseshoes weren't in use back in the old era, it still "feels right" because of the importance of horses to the Celts, especially the warrior class. Different colored ribbons or yarn could be tied to each shoe to identify them and three tosses could be scored in order of proximity.
Archery. The homestead that plays host to our tribe's festivities has an archery range.
Dice. Yes, the requires no skill at all, but could be included to represent the favor of the gods.
Ogham. Three cards with Ogham would be drawn and the person would have to identify them. This would certainly encourage study :).
Riddles. While this is so Celtic (imo), it would also be hard to do. The best way I can think of off the top of my head is to have three riddles and have people write their answers down. Ideally, the riddles could come from Celtic tales, or be based on events, person, gods and such in them.
Drinking. Oh wait... that's not fair. ;) Granted, it would make up for my lack of archery, but I can't participate anyways.
Which brings me to the next point... the druid would have to act as judge and referee.
If you have no clue why I'm talking about any of this (and are curious) go here... http://www.geocities.com/uncleozzi/pagan.htm .