The study of non-modal amplification of distributed body forces in channel flows of viscoelastic fluids has provided useful insight into the mechanisms that may govern the initial stages of transition to elastic turbulence. However, distributed body forces are not easy to implement in experiments and there is a need to examine amplification of localized body forces. In this work, we use the linearized governing equations to examine such amplification in channel flow of viscoelastic fluids. We first identify the wall-normal location at which the impulsive excitations experience the largest amplification and then analyze the kinetic energy of the fluctuations and the resulting flow structures. For a viscoelastic fluid at low Reynolds numbers, the largest amplification occurs for impulses located near the channel wall. Flow structures that evolve from the localized body force at the optimal location stretch out in the streamwise direction in a viscoelastic fluid, unlike a Newtonian fluid in which disturbances merely diffuse in space due to low inertia. For viscoelastic fluids, we observe the development of vortical structures away from the source of impulsive excitation. This feature is less prominent in Newtonian fluids and it may provide a mechanism for triggering the initial stages of transition to elastic turbulence.