This paper considers the joint power-allocation and relay-selection problems in multiuser cooperative communication networks, where one user can only seek a limited number of relays for cooperation. This relay-selection degree bound is of practical significance. The goal is to optimize the relay selection and power allocation in a distributed manner while respecting certain users' quality-of-service (QoS) requirements. This problem is challenging due to its combinatorial nature, even from a centralized perspective, let alone distributed algorithms (or protocols). For this joint optimization problem with inherent combinatorial nature, this paper resorts to a layering approach. Specifically, the optimal power allocation for a fixed but arbitrary relay-selection configuration is carried out in the physical layer while the relay selection is done in the media access control (MAC) layer. The general idea is to run distributed relay-selection schemes based on a time-reversible Markov chain over a distributed power-allocation algorithm in the physical layer. It turns out that these methods can approximately solve this joint power allocation and the relay-selection problem with a certain performance guarantee. More importantly, the resulting solution can be implemented in a distributed manner. Numerical results are also presented to demonstrate the performance of the algorithms.