Motivated by delay-sensitive information transmission applications, we propose an expected achievable rate maximization scheme with a K-block delay constraint on data transmission using a three node cooperative relay network assuming a block fading channel model. Channel information is fed back to the transmitter only in a causal fashion, so that the optimal power allocation strategy is only based on the current and past channel gains.We consider the two simplest schemes for information transmission using a three node (a source, a relay and a destination) relay network, namely the amplify and forward (AF) and decode and forward (DF) protocols. We use a dynamic programming based methodology to solve the (K-block delay constrained) expected capacity maximization problem with a short term (over K blocks) sum power (total transmission power of the source and the relay) constraint. Furthermore, two simple power allocation schemes for high and low SNR situations are proposed. Extensive numerical results are presented for Rayleigh fading channels, including results demonstrating the accuracy of the high/low SNR approximation based power allocation schemes.