In order to satisfy the delay requirements of telecommunication systems, in this paper, we present a cooperative network with the short packet transmission in the Rayleigh fading channel. The desired relay can be implemented as a two-way half-duplex (HD) or a two-way full-duplex (FD). Also, for more accurate satisfaction and reduction of communication delays, sending and receiving with short packets is considered. Effective capacity appropriately measures the transmission rate under the delay constraint. Therefore, it is considered as a performance evaluation criterion here. With a two-way relay, two nodes exchange data with each other using a relay simultaneously. The priorities and requirements of the two nodes are not necessarily the same. Therefore, to increase performance, the system is modeled and solved as a multi-objective problem. In this way, the available power in the network is divided between the relay and two nodes, and the effective capacity of the two nodes is maximized. Depending on the different conditions, the optimal amount of allocated power to relay and nodes is calculated. However, due to the complexity and time consuming calculations, an approximate method which speeds up the calculation is presented. The approximated solution has a very close performance to the optimal allocated power. Finally, various comparisons have been made in different conditions between the performance of two-way HD and two-way FD relays. The improvement of multi-objective power allocation has been shown, especially when the relay is not located in the middle of two nodes.