This work presents joint iterative power allocation and interference suppression algorithms for spread spectrum networks with multiple relays and the amplify and forward cooperation strategy. A joint constrained optimization framework that considers the allocation of power levels across the relays subject to individual and global power constraints and the design of linear receivers for interference suppression is proposed. Constrained minimum mean-squared error (MMSE) expressions for the parameter vectors that determine the optimal power levels across the relays and the parameters of the linear receivers are derived. In order to solve the proposed optimization problems efficiently, stochastic gradient (SG) algorithms for adaptive joint iterative power allocation, and receiver and channel parameter estimation are developed. The results of simulations show that the proposed algorithms obtain significant gains in performance and capacity over existing cooperative and non-cooperative schemes.