According to this Wikipedia article, capital punishment is as old as human society itself, more or less. Therefore, it might prove very difficult to establish that throughout history, a certain nation, in its various transformations, didn't have the capital punishment as part of its legal system.
However, this table, specifying the distribution of capital punishment per nation, states that there are a few nations in which there were non executions since their independence. Some of them have or had the capital punishment as an unused option (in some cases it was abolished at some point), and some (such as Macau or Montenegro) abolished it right from the start. Montenegro's case is interesting: as part of Serbia & Montenegro,the nation had a death penalty. The last execution was in 1992, and in 1995 the penalty was abolished. Montenegro became an independent nation in 2006, and didn't change the abolished status of the death penalty. It appears that a similar case is that of the small island nation Niue, which gained its independence from New-Zealnd after the latter had abolished the capital punishment.