We construct operators t(z) in the elliptic algebra introduced by Foda et al. A_{q,p}sl(2)_c). They close an exchange algebra when p^m=q^{c+2} for m integer. In addition they commute when p=q^{2k} for k integer non-zero, and they belong to the center of A_{q,p}(sl(2)_c) when k is odd. The Poisson structures obtained for t(z) in these classical limits are identical to the q-deformed Virasoro Poisson algebra, characterizing the exchange algebras at generic values of p, q and m as new W_{q,p}(sl(2)) algebras.