We studied spatially isolated single-walled carbon nanotubes (SWNTs) immobilized in a quasi-planar optical λ/2-microresonator using confocal microscopy and spectroscopy. The modified photonic mode density within the resonator is used to selectively enhance or inhibit different Raman transitions of SWNTs. Experimental spectra are presented that exhibit single Raman bands only. Calculations of the relative change in the Raman scattering cross sections underline the potential of our microresonator for the optical control of nonequilibrium phonon populations in SWNT.