We present polynomial-time approximation algorithms for the problem of computing a minimum congestion fault-tolerant redundant assignment of messages to faulty parallel channels. In particular, given a set of channels, each failing randomly and independently with a given probability, a set of messages, and a reliability constraint (1-\epsilon), we seek a redundant assignment that minimizes congestion (i.e. the maximum channel load) and satisfies the reliability constraint (i.e. all messages have a copy on at least one active channel with probability at least 1-\epsilon).