Longer answer - in a hypothetical universe with just the sun and the two planets maybe. Planet B can rest at the L2 Lagrange point. However it is unstable, so any slight perturbation, no matter how small, would push the planet off that point.
In our real universe these perturbations happen all over the place. Even if you have an isolated three body system, tiny gravitational influences from distant stars is enough to destabilitize planet B from L2.
supern00b64 t1_iwtm3qm wrote
Reply to Is it possible for two planets to orbit each other in a way where Planet A is tidally locked to the sun while Planet B is in geostationary orbit on the dark side of Planet A, thus putting Planet B in a constant total solar eclipse? by FenrirButAGoodBoy
Short answer no
Longer answer - in a hypothetical universe with just the sun and the two planets maybe. Planet B can rest at the L2 Lagrange point. However it is unstable, so any slight perturbation, no matter how small, would push the planet off that point.
In our real universe these perturbations happen all over the place. Even if you have an isolated three body system, tiny gravitational influences from distant stars is enough to destabilitize planet B from L2.