You can match the gyroscopic precession of the planet to the orbital period. This would essentially eliminate seasons. But allow your equator to be on a different place than the tropical rain-forests. And there would be no southern ice-cap. And it would be eternally dark at the north pole. think of a northern hemisphere winter.
The easier solution would be to scale the planet up so that the equator is in the tropical rain-forest.
if you look at the stars at night then you may notice them following a circular path. this is from the earths spin. only there are 2 that don't spin but are always at the same pont. these are the poles. but on earth the place of the poles amongst the stars moves in a circle. completing one circle in about every 26,000 years. this movement of the poles is the precession of the earths axis. due to this precession the time it takes for earth to go through its cycle of seasons is about 20 minutes shorter than the time it takes to make a full lap around the sun.
Now for this to happen in a single orbit. One would need a massive star at or near the maximum luminosity. Creating an orbital period in the habitable zone to be much longer than the earths. Long enough for a large offset moon to make the presession match the orbital period. Only the star wouldn't live long enough for life to evolve. Only about a million or so years.
Again the easier solution would be to scale the planet up so that the equator is in the tropical rain-forest.