We describe searches for decays to two-body charmless final states η′η, η′π^0 and ηπ^0 of B^0 mesons produced in e^+e^- annihilation. The data, collected with the BABAR detector at the Stanford Linear Accelerator Center, represent 232 × 10^6 produced BB̅ pairs. The results for branching fractions are, in units of 10^(-6) (upper limits at 90% C.L.): B(B^0 → η′η)=0.2^(+0.7)_(-0.5) ± 0.4(<1.7), B(B^0 → ηπ^0) = 0.6^(+0.5)_(-0.4) ± 0.1(<1.3), and B(B^0 → η′π^0) = 0.8^(+0.8)_(-0.6) ± 0.1(<2.1). The first error quoted is statistical and the second systematic
