Emission from the solar corona in the visible and infrared is dominated by magnetic dipole (M1) emission lines. The magnetic and thermal properties of the coronal plasma influence the polarized properties of M1 lines and offer an opportunity to directly measure the coronal magnetic field. While the optically thin nature of the coronal plasma requires careful interpretation of observations, some differentiated coronal structures, like coronal loops, may offer opportunities for ‘single-point’ inversions to work. Generalizing the analytical formalism of the ‘single-point’ inversion approach introduced by Plowman (2014) for the Fe XIII 10747 / 10798 Å line pair, we show that some combinations of M1 lines contain degenerate spectropolarimetric information which prohibits their application for this technique. Combining polarized atomic modeling based on coronal loop properties with a sensitivity analysis based on photon noise, we discuss using the Fe XIII 10747 Å, Si X 14301 Å line pair as one alternative combination for implementing this technique. We show that at noise levels around 10-4 of the line intensity, magnetic fields with sufficient strength (~25 G) and not severely inclined to the line-of-sight (<35º) can be recovered using this method. The DKIST will feasibly reach such low noise levels while taking spectropolarimetric observations of multiple coronal emission lines at spatial resolutions close to 1 arcsec, comparable to space-based observatories.