  We report inelastic neutron scattering on single crystals of the bilayer
cuprate family La$_{2-x}$Ca$_{1+x}$Cu$_{2}$O$_{6+\delta}$, including two
crystals made superconducting (transitions at 45 and 55 K) by high-pressure
annealing in an oxygen-containing atmosphere. The magnetic excitations in the
non-superconducting crystal have a similar temperature-dependence as those in
weakly hole-doped cuprates. In the superconducting crystals, there is a
near-uniform suppression of the magnetic spectral weight with increasing
temperature; in particular, there are no signs of a spin gap or "resonance"
peak. This is different from the temperature dependence seen in many
optimally-doped cuprates but similar to the behavior seen in certain underdoped
cuprates. We discuss the possible connection with pair-density-wave
superconductivity.
