Fully support it for murder, r*pe, human trafficking, genocide, trafficking and distribution of deadly drugs like fentanyl (which is equivalent to murder in my eyes), and accepting bribery as a government official or embezzlement of public funds over some amount. I really don't see any other way to deal with those kinds of criminals and I can't stand the people who get all high and mighty about "mercy" while dismissing the actual victims.
However, I do think the death penalty needs to be restricted to cases where it is absolutely certain they are guilty of the crimes charged. Beyond beyond a reasonable doubt, there needs to be zero doubt. This alone will spare the vast majority of those criminals and make actual executions extremely rare, but IMO death always needs to be on the table when everyone is absolutely sure they did it.
Additionally, I submit that having life in prison as the only option increases the chance of false convictions because people don't see life in prison as "that serious" compared to death. People will very rightly flip their shit if they find out that an executed person was innocent, but when that same person is imprisoned for decades and is released with their spirit comprehensively broken and with only a few years of their natural life left, people are far more dismissive because they weren't executed. "Oh well that's sad but what can you do? The justice system is imperfect after all, just be glad we didn't execute you." The solution is not to keep people locked up for life on the off chance one of them is innocent, and when one of them is, claim moral superiority about only locking them up for life. The solution is to make absolutely damn sure they're guilty before you sentence them.
Everyone gets hung up on life in prison being "reversible" and have this idealistic idea that if someone is truly innocent, the absolute truth will come out "eventually" and set them free. But look at actual court records and you'll find that in practice it almost never gets reversed even when there is overwhelming evidence of their innocence, and when it does, the courts take their sweet time as if hoping to run out the clock and for the convicted to just die. Courts don't like reopening cases especially for serious crimes because it reflects negatively on them, so you're as good as condemned as soon as the hammer drops whether the sentence is life or death. People like to think of the innocent prisoner as being able to continuously fight for their innocence, but in reality you only get one chance to defend yourself and after that, no one in power will listen to you whether you're alive to speak or not. Innocent people who get their life sentence reversed are the very very rare exception, not the rule, and usually only because their story resonated with the public in a way they cannot forsee or control, and it's the public pressure that gets the courts to reconsider purely in order to preserve their image, not the guilt of potentially sentencing an innocent person. If you're not noticed by the media or your story doesn't resonate with the masses, like the vast majority of innocent convicts, you have no chance of getting out no matter how innocent you are. And the media and public has shown time and time again to be extremely race/culture selective in which convict they pay attention to, so a white person in the West is way more likely to be freed compared to an equally innocent person of colour.