Alexander's answer omitts a few possilbilites. Wikipedia has an article on Co-orbital configuration and you should check that.
And you should note that it includes a discussion of exchange orbits.
Saturn has two co-orbital moons, Janus and Epimetheus, in an exchange orbit.
And you should also consider the possibility of a ring of planets of each mass and equal spacing sharing the same orbit around their star.
The PlanetPlanet blog by astrophysicist Sean Raymond has a section called Ultimate Solar system, with posts designing imaginary solar systems with as many habitable planets as possible.
In the post The Ultimate Engineered Solar System
Raymond is inspired by a scientific paper by by Smith and Lissauer to design an imaginary solar system with several concentric rings of planets in the habitable zone of the star.
So Raymond describes a star system with several such rings of habitable planets in the star's habitable zone.
And remember what Raymond says about the origin of the sysem he designs with rings of planets:
I can only think of one way our 416-planet system could form. It must have been purposely engineered by a super-intelligent advanced civilization. I’m calling it the Ultimate Engineered Solar System.
So if you ever design such a star system, it will have to have been constructed artificially by a highly advanced society.
And in such a ring of habitable planets sharing the same orbit, they would probably always have to be spaced millions of kilometers or miles apart, and probably often tens of millions of kilometers or miles apart, along their sharted orbit. Thus each planet would probably appear a point of light, instead of disc, as seen from even the nearest planets in the ring of planets.
And since the planets would have to be equally spaced and have equal masses, each planet would feel an equal gravitatinal pull from the planets ahead of it in the orbit and from the planets behind it in the orbit.
The spacing of the planets would probably keep their tidal forces on each other low enoughto keep them from tidally locking their rotations.
I don't know whether the planets would be spaced close enough that they would all change the axial titls of each other to zero, resulting in no seasons except for the seasons which might result from the excentricity of the shared orbit, or whether each of the planets might have its won axial tilt, different from the others, and thus different strengths of its seasons.
Raymond also wrote a post discussing cohorts of co-orbital planets which are only arc segments of rings and not complete rings of planets.
According to Raymond's calculations using a cohort of two planets sharing an orbit:
Compared with the 3-Earth case, a system with 2 Earths can even closer. A 2-Earth cohort is stable when the planets are as close as 8 Hill radii.
The Hill radius of the Hill sphere of a planet depends of the mass of the planet, the mass of the star, and the semi-major axis of the planet's orbit around the star.
In the Earth-Sun example, the Earth (5.97×1024 kg) orbits the Sun (1.99×1030 kg) at a distance of 149.6 million km, or one astronomical unit (AU). The Hill sphere for Earth thus extends out to about 1.5 million km (0.01 AU). The Moon's orbit, at a distance of 0.384 million km from Earth, is comfortably within the gravitational sphere of influence of Earth and it is therefore not at risk of being pulled into an independent orbit around the Sun. All stable satellites of the Earth (those within the Earth's Hill sphere) must have an orbital period shorter than seven months.
So if the mass of your planets is 1 Earth mass each, the star has 1 solar mass, and the semi--major axis of the shared orbit is 1 Astronomical UNit (AU), the minimum stable separation of planets in a 2-planet cohort would be 8 Hill radii or a
about 12,000,000 kilometers or about 0.8 AU. The diameter of Earth is about 12,742 kilometers.
At a distance of 12,000,000 kilometers, the circumference of a full circle would be about 75,398,160 kilometers. So a degree of arc at a distance of 12,000,000 kilometers would be about 209,439.33 kilometers wide, a minute of arc would be about 3,490.6555 kilometers wide, and a second of arc would be about 58.177591 kilometers wide.
The diameter of Earth, 12,742 kilometers, would be 219.01903 arc seconds or 3.6503171 arc minutes.
The angular resolution of the naked eye is about 1′;
So if two Earth sized co-orbital planets were 12,000,000 kilometers apart, they would appear as tiny objects only a few arc seconds wide, much smaller than Earth's Moon appears. And if the two planets were separated by several times 12,000,000 kilometers they would appear a mere points of light from each other.
If the tidal forces of the two planets on each other were strong enough, each would become tidally locked to the other. One side of each planet would permanently face the other, and the other side would permanetly face away from the planet. The direction between the two planets would be appoximatley at right angles to the direction between them and the star, so each of the two planets would also have one side which faced the star with eternal light and heat and one side which faced away from the star with eternal darkness and cold.
So each planet would have four points approximately equally spaced around its circumference. The lst point would be eternally facing the star with the othr planet low on the horizon, the 2nd point would eternally face away from the other planet and the star would always be on its horizon, the 3rd point would eternally face away from the star with the planet low on the horizon, and the 4th point would eternally face the other planet with the star low on the horizon.
Or maybe the two planets would be far enough away from each other that their tidal forces would be too weak to tidally lock them and they would rotate at a normal rate.
I don't know how to calculate the tidal locking forces.
Anyway, I hope these two suggestions might be useful to you.