Electronic coherence transfer has been detected in only a small number of systems despite the potential impact of these dynamics on natural and artificial light harvesting. Nonlinear spectroscopies designed to probe the dynamics of electronic coherences are challenged by signal emission associated with electronic populations. This paper presents a newly developed nonlinear laser spectroscopy capable of measuring intraband electronic coherences (i.e., for pairs of single exciton states) in molecular aggregates with full suppression of undesired signal components. In comparison with methods applying all-femtosecond laser pulses, the present experiment. uses both narrowband and broadband pulses to obtain similar information with a greater than 360-fold faster data acquisition rate. In addition, the technique enhances spectral resolution with experimental control of the measured line widths. High instrument throughput facilitates the comparison. of measurements for a wide variety of materials. As the first application of this technique, we investigate the dynamics of intraband electronic coherences in double-walled cylindrical molecular aggregates possessing five slightly different morphologies controlled by varying the solvent conditions. Interfering coherences associated with pairs of exciton states give rise to well-resolved quantum beats in the measured signal fields. In addition, coherence transfer processes are investigated using a superposition of tensor elements (i.e., an analogue of probing population transfer with pump-probe anisotropy). The comparison of experimental measurements and calculations based on a theoretical model supports the finding of coherence transfer processes terminating in an electronic coherence between the inner and outer cylinder excitons.