Most terrestrial batteries suffer from degradation from not being used as well as wear from use.
One of the longest known standalone power supplies would be the Radioisotope Thermoelectric Generators (RTGs) used in the Voyager spacecraft. Thirty-four years after launch, they are providing 57% of their rated output. Based on that, they will most not likely reach one century of operation.
There is the possibility of coupling a mechanical drive system to some form of generation. In the case of a time capsule, if it was suitably located hydroelectric generation would be a possibility. Depending on the environment for storage, a thermocouple might be usable to supplement the primary power.
In order to reach the goal of a century, a mechanical watch mechanism might be a better bet for the timing - if you can find a power source with sufficient shelf life to wait to be activated.
No matter which method you use to power it, you will have to take a note from spacecraft design, and make the entire system redundant, such that a failure of 50% of the components would still leave it in a usable state.