The orbital mechanics works. As mentioned, a 1:1 orbital resonance. https://en.wikipedia.org/wiki/3753_Cruithne is a good example. If you look at the charts, it makes a close approach to Earth once a year, but how close these approaches are varies over a few centuries.

The question is whether such a body can preserve enough cometary activity to look like a comet to the naked eye. Any object in a 1:1 orbital resonance can never get more than 2AU from the Sun so it doesn't get any real break from the solar heating that drives cometary activity. Active asteroids, also known as main belt comets, are known, but most orbit more like 3AU out.