Natsume and Natori. In one episode of the anime, Natori asks Natsume to go to the hot springs with him, and shows up at his house with a bouquet of roses. It does not help that Natori is voiced by Akira Ishida, who's voiced a number of characters known for their Ho Yay (Kaworu Nagisa from Neon Genesis Evangelion, Fisheye from Sailor Moon, Xerxes Break from Pandora Hearts, Cho Hakkai from Saiyuki, Aru Akise from Mirai Nikki).
Same episode: Natori mentions to Natsume that if constantly lying to his foster family about the Youkai ever becomes too difficult, he can always come to him (please note, their futons are right next to each other at the time.)
Though taken another way (given that Natori had just been asking whether Natsume was happy with his foster parents), this has completely different connotations.
Chapters 60 through 62, in which Natori is way more concerned for Natsume than usual. When they first meet in chapter 60, it's when Natsume falls from a ladder and Natori has to catch him with his customary sparkles. Natori even admits that if Natsume were doing exorcist work, his heart would probably explode from all the worrying. And it looks like Natsume has even acquired a tolerance for Natori's cheesy film roles. Natori kind of ruins the whole thing at the end of chapter 62 by hinting that he's found out about the Book of Friends and showing the creepiest, most predatory grin ever, but such things happen.
In the first episode of Zoku, Natsume commented on the Lord Youkai he had recently freed as being really cute.
Matoba/Natsume (though this could also enter Foe Yay territory). The second episode of the fourth season ramps it up by having Matoba invade Natsume's private space as he inches in on Natsume and practically whispers in his ear, in a "I have you now my pretty" manner. He also seems to enjoy grabbing Natsume by the wrist. And in the manga, he claims that he has written an "uncharacteristically long letter" to Natsume in attempt to persuade him to join the Matoba clan.
Tanuma/Natsume. In a humorous scene (Season 3, Episode 10), both awkwardly blush and smile at each other as the background turns a shoujo manga pink.
Tanuma sure seems intent on learning how Natsume sees the world. Look, they're practically sparkling at one another And 7th episode of 4th season overflows with it (all that hand grabbing and overprotective-ness)
They also have a good amount in Chapter 28.
The anime equivalent last episode of the first season had the end card jokingly translated as "Thank you for watching Natsume Gay-jinchou, or Natsume's Gay Best Friend" by one fansub group because of their near-sparkling at one another throughout said episode.
If Nyanko-sensei/Madara's default form was a human, there wouldn't be any debate about the fact that his constant tsundere attitude towards Natsume would instantly turn into very obvious Ho Yay. Not to mention he spends more time with Natsume than anyone else in the show. Hence why a lot of Madara/Natsume pairings in doujins or fanfics have Madara in a personified human form.
At the end of Season 1 Episode 8, Nyanko-sensei said to Natsume even if Natsume can't see youkai anymore, he wouldn't let Natsume go until he gets the Yuujinchou when Natsume dies. Again at the end of Season 2 Episode 1, Madara refused to return with Benio and said he wanted to wait through the brief moments until Natsume's life end. Both occasions are him essentially saying he wants to be with Natsume for the rest of Natsume's life. And on both occasions, Natsume replies smiles in clear acknowledgement.
And once again at the finale of the fourth season, after denying having watched through Natsume's flashbacks and claimed (not very convincingly) to not care about his memories, Madara makes another remark on how he's only going to stay with Natsume until he gets the Yuujinchou. Another, just Madara's way of saying he's going to stay with Natsume for the rest of the boy's short, mortal life, except this time, even Madara himself said it with a warm, loving smile.
Madara constantly repeating that Natsume is "his". The most touching of those scenes is at the end of Season 3 Episode 12, when Madara drove away a youkai threatening to kidnap Natsume, who also tried to claim Natsume for her own. This and the whole of Season 2 Episode 7 just shows that for all of Madara's denial, he genuinely cares very deeply about Natsume.
Natsume does also return his feelings. One notable example is at the beginning of the fourth season where Matoba threantened to kill a debilitated Nyanko-sensei, Natsume's first reaction was to protect the unconscious Nyanko-sensei, not grab his bag with the Yuujinchou inside, making his later statement about how his duty is to "protect the Yuujinchou and not Nyanko-sensei" a rather tsundere lie.
Natsume spends the end of both the third and especially the fourth season with mostly just Nyanko-sensei, showing just how important the two had become for each other. For all the hopeless Big Eater he is, Nyanko-sensei didn't actually get annoyed at having lost the chance to go to the Udon shop, he cares enough for Natsume to know just how important the trip was for him. One can only wonder if Natsume's childhood would have been a bit better had he met Nyanko-sensei sooner.