I finally got the chance to play through Castaway Stories this week-end.
The villagers do ask for specific items or actions and when you complete them, they immediately befriend your sim. I'll list them here incase anyone else is interested.
First group of villagers
Kiri - wants your sim to light the trash pit on fire.
Timoti - wants to be invited to play chess with your sim.
Orama - wants a singing stone, which you can get by playing the singing stone game and winning 10 consecutive rounds.
Emobi - wants your sim to repair the broken exercise equipment in the village.
Second group of villagers
Tumata - wants your sim to play the drums.
Rainui - wants your sim to push her on the swing.
Ahio - wants your sim to spearfish and catch a fish.
Akolo - wants your sim to catch fireflies and give him the jar.
Be sure to chat with each first, they'll give you clues to what they want and don't forget to recieve your gift from each.
I'm really enjoying this little side game and I hope this helps someone else : )
... Anybuddy know a cure for Alien withdrawl?