Yes, members of the E.U. should be allowed to institute the death penalty just as the United States and many other countries have the death penalty. The death penalty is reserved for the most serious crimes and serves to deter criminals from committing these crimes. Members of the E.U, should be allowed to have the death penalty for the worst crimes.
Europe and the rest of the world needs to be moving forward, not backward. Instituting the death penalty would be moving backward. The death penalty also isn't really a deterrent to terrorism or military coups, since we've seen those events take place primarily in countries that do have the death penalty.
Reintroducing the death penalty in E.U. member countries is unlikely to act as deterrent. Many of those who commit acts of terrorism are already prepared to die for their beliefs and consider themselves martyrs. For these extremists, death has no fear and execution by the state is more likely to encourage other fanatics to seek revenge against innocent civilians, setting up a vicious cycle.
Not allowing the death penalty has been one of the most positive and progressive actions that the EU has undertaken. Reversing this action, even for one country would be a step in the wrong direction. Turkey should reconsider reinstating the death penalty in order to avoid leaving the European Union.