Observation of B^{+}→Ηρ^{+} and Search for B^{0} Decays to Η′Η, Ηπ^{0}, Η′Π^{0}, and Ωπ^{0}

We present measurements of branching fractions for five B-meson decays to two-body charmless final states. The data, collected with the BABAR detector at the Stanford Linear Accelerator Center, represent 459 x 10(6) B (B) over bar pairs. The results for branching fractions are, in units of 10(-6) (upper limits at 90% C.L.), B(B+ -> eta rho(+)) = 9.9 +/- 1.2 +/- 0.8, (BB0 -> eta(')eta) = 0.5 +/- 0.4 +/- 0.1(<1.2), B(B-0 -> eta pi(0)) = 0.9 +/- 0.4 +/- 0.1( <1.5), B(B-0 -> eta(')pi(0)) = 0.9 +/- 0.4 +/- 0.1(<1.5), and B(B-0 -> omega pi(0)) = 0.07 +/- 0.26 +/- 0.02(<0.5). The first error quoted is statistical and the second systematic. For the eta rho(+) mode, we measure the charge asymmetry A(ch)(B+ -> eta rho(+)) = 0.13 +/- 0.11 +/- 0.02.