In this paper, we study an optimum power allocation problem for expected achievable rate maximization in a typical three node cooperative relay network with slow block fading channels. A long term average power and an outage probability threshold serve as the constraints on the problem. This is motivated by the fact that in many applications, a mixture of delay-sensitive and -insensitive data are transmitted and either maximizing expected achievable rate or minimizing the outage probability would probably not provide the desired solution. The problem considered in this paper (known as the "service outage based rate and power allocation" problem in literature) thus achieves a tradeoff between the two extremes of ergodic capacity and outage capacity. We show that the optimum power allocation scheme is a switched policy between two deterministic policies. Extensive numerical results are presented to demonstrate the benefits of cooperation as opposed to that of non-cooperation or direct transmission. We study the performance of the two simple but popular relaying schemes, namely, the amplify-and-forward and decode-and- forward protocols. It is seen that these relaying protocols are extremely resilient against demanding outage probability constraints over a range of basic rate requirements and average power constraints.