The protagonist can start Dojima's Social Link as early as May 6th. He can be found inside the Dojima Residence during the evenings after the protagonist finishes the story's current dungeon or between story dungeons.
In Persona 4, the deadline to complete Dojima's Social Link is November 2nd, as it will become unavailable for the rest of the game after this. In Persona 4 Golden, his Social Link becomes available again starting on January 24th.
Dojima gives the protagonist a Coffee Mug when the Social Link is maxed, which enables the fusion of Kohryu.
To initiate Dojima's Social Link Rank 4, the protagonist must reach Rank 3 Expression (Persuasive).
Rank 4
Response
Points (W)
Points (W/O)
"All we've got is instant, though. How do you take it?"
Black.
+3
+2
With cream.
+3
+3
Cream and sugar.
+3
+2
Surprise me.
+3
+3
"Go watch TV with Nanako. I'll bring it to you when it's ready."
You don't have to do that.
+3
+2
Thank you.
+2
+1
Rank 5
Rank 5
Response
Points (W)
Points (W/O)
"Oh... Sorry, I wasn't talking about you."
Looking for something?
0
0
Can I help?
+3
+2
Working at home?
+2
+1
"It's late. Go to sleep."
Are you okay?
+3
+2
What was that about?
+2
+1
But Nanako?
+3
+2
Rank 6
To initiate Dojima's Social Link Rank 6, the protagonist must reach Rank 4 Expression (Touching).
Rank 6
Response
Points (W)
Points (W/O)
"Let's stop there."
Let's not.
+2
+1
Even if it's about family?
+2
+1
Then let's go outside.
+3
+2
"I don't need a private life to do that. ...Nanako will understand."
You're right.
0
0
Is that what she wants?
0
0
That's just an excuse.
0
0
Rank 7
Rank 7
Response
Points (W)
Points (W/O)
"I can do that anytime."
When is 'anytime'?
0
0
This is more important, huh?
+2
+1
Rank 8
Rank 8
Response
Points (W)
Points (W/O)
"Sorry, but my hands are full here."
Working at home again?
0
0
Buying a new car?
0
0
Want some coffee?
+3
+2
"Do you understand why?"
Because of Nanako.
+2
+1
Because her killer's loose.
+2
+1
Because you're a coward.
+3
+3
Rank 9
Rank 9
Response
Points (W)
Points (W/O)
"Er... Sorry about making you go along with this today."
I don't mind.
+2
+1
It was fun.
+3
+2
Ask me next time.
+2
+1
"That's why I used revenge as an excuse to spend time away from her..."
Was it hard?
+3
+3
Do you regret it now?
+2
+1
You've stopped running?
+3
+2
Rank 10
Rank 10
Response
Points (W)
Points (W/O)
"This is your personal mug. Write your name on it later."
Thank you.
+3
+2
What am I using now?
+2
+1
My name? That's okay...
+3
+3
"Sorry, but take care of Nanako."
Go get 'em.
+3
+3
Be careful.
+3
+3
Leave it to me.
+3
+3
Other
Gardening, 6/12
Garden, 6/12
Response
Points (W)
Points (W/O)
"Are you regretting letting Nanako talk you into this yet?"
To be honest, just a little...
0
0
Not really.
+2
+1
I'm glad I did this.
+3
+2
Notes
In Golden, the protagonist can increase Dojima's Social Link progression by 1 point by saying "This is a nice bike." on 06/09. If the protagonist has a Persona of the Hierophant Arcana in his stock, the progression will be 2 points.
In Golden, agreeing to help Nanako with her homework on 1/28 will increase Dojima's Social Link progression by 2 points, and will automatically increase by 2 points each on the evenings of 1/29 and 2/4.