InverseLaplaceTransform and convolution

Is there a reasonable way to map general terms like this

In[50]:= InverseLaplaceTransform[x[s] y[s], s, t]

Out[50]= InverseLaplaceTransform[x[s] y[s], s, t]

to a convolution integral in the time domain?

Mathematica evidently doesn’t automatically do

L^-1{x(s)y(s)}=(X•Y)(t)