A state-dependent degraded broadcast diamond channel is studied where the source-to-relays cut is modeled with two noiseless, finite-capacity digital links with a degraded broadcasting structure, while the relays-to-destination cut is a general multiple access channel controlled by a random state. It is assumed that the source has non-causal channel state information, the relays have no state information and the destination may or may not have state information. First, the capacity is found for the case where the destination has access to the state sequence. It is demonstrated that a joint message and state transmission scheme via binning is optimal. Next, for the case with state information at the source only, lower and upper bounds on the capacity are derived for the general discrete memoryless model. Achievable rates are then computed for the case in which the relays-to-destination cut is affected by an additive Gaussian state.