  We construct the {\it quasi-stationary} (QS) probability distribution for the
Domany-Kinzel stochastic cellular automaton (DKCA), a discrete-time Markov
process with an absorbing state. QS distributions are derived at both the one-
and two-site levels. We characterize the distribuitions by their mean, and
various moment ratios, and analyze the lifetime of the QS state, and the
relaxation time to attain this state. Of particular interest are the scaling
properties of the QS state along the critical line separating the active and
absorbing phases. These exhibit a high degree of similarity to the contact
process and the Malthus-Verhulst process (the closest continuous-time analogs
of the DKCA), which extends to the scaling form of the QS distribution.
