Short answer, what you are asking for is basically impossible.
Longer answer, here is the reason why. But there is something which might possibly give a somewhat similar situation.
The third paragraph in section 2 of the article "Exomoon Habitability Constrained by Illumination and Tidal Heating" says:
The longest possible length of a satellite's day compatible with Hill stability has been shown to be about Pp/9, Pp being the planet's orbital period about the star (Kipping, 2009a).
That is in the case of a natural satellite tidally locked to its planet, so that the satellite's month and day are the same length. So that means that a natural satellite or moon with a stable orbit has to orbit the planet at least 9 times in each year of the planet.
So a natural satellite that orbits the planet with an orbital period or month equal to the length of the planet's orbital period around its star, or year, will not have a stable orbit and will probably escape from the planet's gravity and orbit the star independently (and possibly collide with and devastate the planet later) very soon by geological standards. By the time that multi celled lifeforms live on the planet, or intelligent life evolves, or the planet develops an oxygen-nitrogen atmosphere breathable for humans, the moon will be long gone.
This is the source the quoted article gives for the sttement:
Kipping D.M. Transit timing effects due to an exomoon. Mon Not R Astron Soc. 2009a;392:181–189.
So if the orbital stability equations are correct, neither of the moons can orbit the planet with a year-long orbit. No matter whether the planet's year is 1 Earth day or 500 Earth years long, the outer moon with the longer month must orbit the planet at least nine times per planetary year, and the inner moon with the shorter month must orbit more times than the outer moon.
But all is not lost. There is something called a synodic period. In the case of two satellites of a planet their synodic period could be the time between successive moments when the satellites are in the same position relative to each other. It could be the time between successive moments when the inner satellite is 90 degrees ahead of the outer satellite, or the time between successive moments when the inner satellite eclipses the outer satellite, for example.
The synodic period may take many orbits of the two satellites until they return to the same (relative) position.
There are four astronomical seasons on Earth, although various regions might have different numbers of climatic seasons for various reasons. But if your fictional planet as an axial tilt like Earth's most regions in the temperate zones should have four seasons, spring, summer, autumn and winter.
So if the two moons have synodic periods of the right length, there could be four synodic periods per year, and the natives of the planet might think that the synodic periods that roughly coincide with the change of seasons somehow cause the change of seasons.