I'll offer a substantially different approach from what has been said so far. The orbit of your planet doesn't necessarily need to be eccentric or instable and neither does it need a rapidly oscillating axis of rotation.
The cause of these fluctuations in temperature could be similar to our earth's ENSO which is a global phenomenon where the surface temperature on the equatorial pacific ocean fluctuates erraticly over a period of 2-7 years. These differences can easily reach 3°C between warm and cold periods and are extremely hard to predict.
Essentially, the west pacific ocean is generally warmer that the east. Every 2-7 years, this warm spot begins to expand and drifts east. The upward flow of air this causes over the pacific ocean causes more eastward wind and less westward wind, which in turn accelerates the eastward drift of this warm surface water.
How exactly this process then reverses is not entirely clear as is the cause for this phenomenon and what exactly is needed for a cycle like this to exist is also a difficult topic. So I suggest you do some further reading there.
Some prerequisites seem to be a large ocean and not too many temperature fluctuations apart from these effects. (hence why it occurs at the equator).
I can imagine that on a planet where there are two large land masses, seperated by a huge ocean, east to west (and another smaller ocean on the other side of course) that has a small axial tilt (and thus barely noticable traditional climates), these effects could cause what would seem like irregular seasons.
disclaimer: I am by no means an expert on this topic, so please do tell me or edit if I got something wrong.