  We search for B0 meson decays into two-body combinations of K0, eta, eta',
and phi mesons in 324 million B Bbar pairs collected with the BaBar detector at
the PEP-II asymmetric-energy e+e- collider at SLAC. We measure the following
branching fractions (upper limits at 90% confidence level) in units of 10^{-6}:
Br(B0->eta K0) =1.8+0.7-0.6 +-0.1(2.9), Br(B0->eta eta)=1.1+0.5-0.4 +-0.1(1.8),
Br(B0->eta phi)=0.1+-0.2 +-0.1(0.6), Br(B0->eta' phi)=0.2+0.4-0.3 +-0.1(1.0),
Br(B0->eta' eta')=1.0+0.8-0.6 +-0.1(2.4), where the first error is statistical
and the second systematic.
