 If you liked
Natsume Yuujinchou
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 ...then you might like
Ushio to Tora (TV)
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A young boy releases a Youkai and they become partners with the intent of the yokai eating them in the end. In both a friendship type bond begins to form between them. There's also a similar "youkai of the week" thing going on. Ushio to Tora is more actiony than the slower paced Natsume Yuujinchou however.
Young boy has a family that is tied to supernatural and comes to a possesion of a powerful item. Youkai are frequently attacking him thanks to this item. This boy also releases a powerful youkai by accident which they team up with as that youkai wants this item. That youkai is defending the boy in a tsundere kind of way as they frequently say that it would be better for that boy to just die already as that would mean the item would be free to take. So if you're looking for this kind of relationship between the protagonist and a monster, watch those two
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Both are talking about yokai.
Just like in Natsume Yuunjinchou, the protagonist has a protector with almost the same behavior(Madara and Tora).
The main character is making friends as long as the story goes.