Courage will be "greatly" increased if you buy the books from the book store every month. They are only available one day each month so you need to check when. The "timid teacher" series, though, will raise your understanding. The book store is located in South of the Shopping District.
In the North district, look at the bulletin board. There will be jobs. If you take the job as an envelope maker, you can raise your diligence. The other way to raise your diligence is by constructing models (you have to raise your Hermit S Link in order to get the option) or by eating at the cafe on rainy days (which will increase all of your stats)
From: onionring1988or by eating at the cafe on rainy days (which will increase all of your stats)
Actually only 3 of 4 at random. The 5th, expression, is left out sadly. Which is a pain because Nanako needs "enthralling" after a certain S Link rank. Anyway, it's better to do those that increase stats along with S Links:
- Diligence - Obviously the sports team. In your bedroom, envelope construction & building a model once you reach that Hermit S Link rank. - Courage - The hospital nurse S Link. Same board where you find the last 2 above, but available after May 25th. Along with making Mooroka look like a pansy on your first day of school & sometimes random food in the fridge at home. Be aware some food won't give an increase or "spend time". Basically the tastier it sounds, the more of a chance that happens. Something that you though used to be a pear = a good increase in courage - Knowledge - You'll probably max this out over the course without doing much else to increase it. Just answer correctly in class when you're asked a question + listen to the lectures. Higher knowledge is always good though, better rewards from Ms. Sofue (egyptian teacher) & Dojima gives you more money. Nanako will give you a nice accessory if you're placed at the top only. - Understanding - Doing the origami sidejob from the board will increase this. You'll need rank 5 in this before even starting the tutoring job (May 25th). - Expression - Drama or music club, doesn't matter.
All of them can be increased with books you read on the couch in your room along with rare random convos through the game, both main story & other S links. If you have absolutely nothing to do on a rainy day, eating at Aiya (north shopping district, directly left of the job board) will increase 3 of 4 stats mentioned earlier. Otherwise eating at Aiya on a sunny or cloudy day will greatly increase 1 of 3 stats (courage, understanding OR diligence), the meal available for 1 of those 3 depends on the day of the week.
Forgot about those 2, thanks for pointing them out. Thought tutoring raised knowledge instead (but I didn't care much for his story, almighty triangle) & only used the cat once for that hermit sidequest, but yeah the cat raises understanding & expression according to the DJ guide.
Also, knowledge can be greatly increased on rainy days. Go to the library on the 2nd floor of the school. The week before tests the team will be asking if you can help them study which will give the same effect but with an S link increase towards one of them. But like I said earlier you'll most likely reach max knowledge by the end of the game answering questions, choosing certain responses etc. so use your rainy days for eating at Aiya, the shrine to complete an ema request/boost an S link after getting hermit to rank 10 or just going through a cleared dungeon for sidequest items + optional boss, are much better. Study with your teammates when you feel you need to boost an S link & they're available the day after for the rank increase.