You'll want to provide good incentives and even contingency if the player doesn't win as to why the NPC would invite him to the manor. First off, I'll devote this to the four generic character classes--fighter, cleric, wizard, and rogue.
Fighter--events he could compete. The fighter can compete in any of the events that would appeal to his specialty--combat, archery, weight lifting, arm-wrestling, dire-bear wrestling, etc. If he wins, he gets the invitation. If he loses, he still gets the invitation because the winner is a real a-hole (more on that below). Motivation for being in the contest is that these have the largest coin purses with no entry fee.
Cleric--even though it's in honor of Pelor, clerics of other faiths are allowed to come and prosyltize with the hopes of obtaining new converts, so long as those faiths are not against Pelor or his teachings. The cleric makes Diplomacy checks or allow the player to roleplay out a short sermon. This will impress the NPC as he's moved the most by the cleric's oratory. Clerics would be directed by the elders of their faith to attend this to get converts as it's important for them. Just so the player doesn't hog the spotlight, put them on a timer in which they have 1 minute to say cool stuff about their god.
Wizard--the apprentice has one last test before his master will let him go-he must compete is the spell competition. The wizards will be judged by their performance of spells and how well they did. Many other wizard masters will be there to judge the wizard. You can set some kind of Concentration or Spellcraft check to play against the competitors and if the wizard wins, his skill wows the judges and the crowds. If he loses, he still catches the eye of the NPC who could be a wizard and knows a good one in the making.
Rogue--rogues can participate in the acrobatic contests (the wet logs spring to mind, tightrope), archery, or the fighter competitions. Another motivation is that the rogue may want to join the Thieves Guild. This is a good proving ground just to see if the rogue is good. If he wins, he's got the attention of the Thieves Guild for now. If he loses, don't let the door hit you on the way out. But this would be the motivation for joining. Other motivation is that the acrobatic contests also carry large purses with no entry fee.
Setting up the contests will be easy and should stack the deck in each player's favor. Hopefully they are playing to their strengths have a good modifier to their rolls. Their competitors will suck and have +1 or +2 if at all (1st level commoners yo!).
Give your players a chance to win. If they win on the first throw, that's the contest. They won. If they lose, tell them that they have to do "2 out of 3." If they blow that, well, they came in 2nd place.
Complications--say your players refuse to participate in the event or they lose? Well, you can have other things like:
1. Spot the Cheater. Say the rogue didn't want to participate, have him roll a Perception check. The rogue spots a cheater in one of the contests. If the rogue calls out the cheater, the cheater is quickly caught and the NPC congratulates the rogue on his "eagle eyesight". Invitation follows.
2. The a-hole winner. Not every one of your players will win if you make it challenging. However, the winner of the contest is a real a-hole. Make it known to the players (he grabs the prize, pushes the livery kid over who presented it to him, grabs a kiss from the maiden despite her protestations, etc). The NPC will be decidedly unimpressed with the winner's attitude and will issue invitation to the 2nd place guy.
3. I do protest! The winner of a contest gets a kiss from the most beautiful maiden in the village in addition to the prize. The a-hole winner (above) wants some sugar, but was such a jerk that the maiden refuses the guy because of his poor manners. Here the guy can be really difficult and one or more of the players can step to defend the maiden's honor. If you want go into combat, you can otherwise, the guy backs down when one or more of the PC's step into the fray. This impresses the NPC.
Strong motivations is to have large purses for simple contests. Yeah 20 gp may be realistic, but this is D&D, play for 200 gp - 500 gp per contest. It will allow them to buy some nice swag before they really start adventuring, but nothing to break the bank or adventure just yet. However, only one contest per player.
