It is shown by both analytical methods and numerical simulations that extremely long living spherically symmetric oscillons appear in virtually any real scalar field theory coupled to a massless dilaton (DS theories). In fact such ``dilatonic'' oscillons are already present in the simplest non-trivial DS theory — a free massive scalar field coupled to the dilaton. It is shown that in analogy to the previously considered cases with a single nonlinear scalar field, in DS theories there are also time periodic quasibreathers (QB) associated to small amplitude oscillons. Exploiting the QB picture the radiation law of the small amplitude dilatonic oscillons is determined analytically.