To my limited knowledge, as far as I can remember, the prayer for the air, fruits, plants, rivers, seas, etc. (prayer for nature) changes every season. There's a general prayer for nature, and there's three different prayers for nature for three different seasons in the year.
Just in case anyone is curious, yes, in Egypt there is (or was) only three seasons: innundation (when the Nile flooded), emergence (when the floods receeded and plants were grown) and harvest. The high dam put an end to all that.
Really in the rites of the Coptic Church, I can't think of anything else in the Basilian liturgy itself that changes during the year. Perhaps, music and hymnology changes, such as the 'Hitens' (Through the intercessions/prayers, sung after the Thanksgiving prayer), Post-Catholicon (post Catholic Epistle) hymn; Apasmos Adam (after the Prayer of Reconciliation) and Apasmos Vatos (after Meet and Right); Psalm 150 refrains and music, but the liturgy itself is the same for the most part. Sometimes the priest likes to mix and match anaphoras and prayers from other liturgies into the liturgy of St. Basil like the prayers before and after the Litanies, and sometimes you will hear him sing "Je Nai Nan" (Have Mercy) after when he says, "And those who dwell therein in God's faith," within the Litanies themselves, right before the prayer for nature.
That's all I can think of at the moment.
The verses inserted between the Holy God verses change for at least Feasts of the Lord.