Ultra-sensitive greenhouse gas sensors for CO2, N2O, and CH4 gases based on Fano resonance modes have been observed through periodic and quasi-periodic phononic crystal structures. We introduced a novel composite based on metal/2D transition metal dichalcogenides (TMDs), namely; platinum/platinum disulfide (Pt/PtS2) composite materials. Our gas sensors were built based on the periodic and quasi-periodic phononic crystal structures of simple Fibonacci (F(5)) and generalized Fibonacci (FC(7, 1)) quasi-periodic phononic crystal structures. The FC(7, 1) structure represented the highest sensitivity for CO2, N2O, and CH4 gases compared to periodic and F(5) phononic crystal structures. Moreover, very sharp Fano resonance modes were observed for the first time in the investigated gas sensor structures, resulting in high Fano resonance frequency, novel sensitivity, quality factor, and figure of merit values for all gases. The FC(7, 1) quasi-periodic structure introduced the best layer sequences for ultra-sensitive phononic crystal greenhouse gas sensors. The highest sensitivity was introduced by FC(7, 1) quasiperiodic structure for the CH4 with a value of 2.059 (GHz/m.s−1). Further, the temperature effect on the position of Fano resonance modes introduced by FC(7, 1) quasi-periodic PhC gas sensor towards CH4 gas has been introduced in detail. The results show the highest sensitivity at 70 °C with a value of 13.3 (GHz/°C). Moreover, the highest Q and FOM recorded towards CH4 have values of 7809 and 78.1 (m.s−1)−1 respectively at 100 °C.