Hey, I figure it's been awhile since I posted this, and it's quite a hard procedure to figure out on your own, so here's how to get the Couple's Mask!
Get the Kafei's Mask from Madam Aroma, and she will tell you to find Kafei and give you a mask to help you ask about his whereabouts.
On the first day after Anju recieves her letter from Kafei at the Inn desk, talk to her wearing the Kafei mask. You should meet her later that night. If you don't have an Inn key, turn into a deku and use the flower by the Treasure Chest game to get up to the other entrance.
Meet her in the Kitchen at 11:30PM. She will give you a letter for Kafei. Drop it in a mailbix before the postman makes his collecting rounds.
On the second day, at 4:15 PM, yyou'll be able to eneter the door in the Laundry Pool. It is the back entrance to the Curioisity Shop. Talk to Kafei and he will give you the Pendent of Memories for Anju. Take it to her immediately.
Enter the back door to the Curiosity shop again, between 1 and 10 on Day 3. The Curiosity Shop owner will be there, Talk to him and he will give you the Keatan Mask and a letter for Madam Aroma.
Give the letter to the Postman and he will deliver it for you. If you talk to him after he delivers it, he will giveyou his Postman's Hat.
Go to Ikana and run to Sakon's hideout. Kafei will be hiding behind a group of rocks. Hide there with him until Sakon comes. Follow him into the hideout.
Navigate through the rooms. Kafei will hit the blue switches, they let Link out of his room. You have to kill an enemy. You have to do this until you get to the sun's mask at the end of the conveyor belt.
After Kafei takes the Sun Mask, warp back to Clock Town by playing the Song of Soaring. Run into the Inn and enter the room at the top of the stairs. Wait there with Anju until Kafei comes very close to Midnight. The Sun and Moon Masks will unite to form the Couple's Mask. They will give it to you as a present for reuniting them.