This experimental study explored combustion dynamics associated with coaxial laminar jet diffusion flames in the presence of acoustic excitation. The methane-air jets burned inside a closed cylindrical waveguide at atmospheric conditions, where flame behavior was captured via direct high-speed visible imaging. As the acoustic forcing increased at a fixed frequency in the vicinity of a pressure node associated with a standing wave, the flame underwent a transition from sustained oscillatory combustion (SOC) to periodic lift-off and reattachment (PLOR) and eventual flame blow-off (BO). The nature of this transition and flame-acoustic coupling was explored by varying a wide range of experimental parameters for five different coaxial jet geometries, including the jet Reynolds number, outer-to-inner jet velocity ratio, coaxial jet wall thicknesses and diameters, and amplitude of acoustic excitation. Flame-acoustic coupling processes were observed to vary significantly based on the annular-to-jet area ratios and tube wall thicknesses under similar flow conditions. Analyzing the spatiotemporal flame dynamics via proper orthogonal decomposition (POD) of high-speed imaging data revealed different signatures of the transition process, including abrupt changes in the mode energy distribution and a significant increase in the complexity of the phase portraits when flame dynamics involved additional time scales. Results from this study suggested that increased annular-to-inner area ratio and velocity ratio can greatly enhance flame stability and resistance to blow-off, with wall thickness playing a lesser role.