If you're looking for anime similar to Neko Koibito, you might like these titles.
What's Michael? Michael is a cat. A cat that is inexplicably attracted to the smell of raw fish, yet horribly repulsed by the smell of toothpaste. A cat that, in a dogfight with a fly, will strafe his master in her sleep. In short, Michael is a cat like any other cat.
The manga centers on a woman who is getting on in years, but all her cats think she's a man so they call her Ojii-chan. One day a brazen cat named Tsushima appears in Ojii-chan's yard.
A lady lives a quiet life with her two loves: alcohol, and her many cats. She’s had many of the latter over the years including an oft-grumpy Scottish Fold mix and Poko, an orange ball of energy who was abandoned as a kitten and saved to live another day. Whether the kitties are playing with cotton gloves, getting to know each other or causing mischief, they and the lady live happily together.