In its current system? No. My feelings are dual: On one hand, liberal advocates have utterly cucked the system and have managed to turn the death penalty sentence into an infinite money generator for lawyers to gum up the judicial system in appeal after appeal so that by the time a prisoner is executed, he's spent years on death row and sucked up perhaps millions of taxpayer money. On the other, I feel that personally in this day and age that the "standard for evidence" to go ahead with the death penalty is far too low. It's an irreversible decision once carried out, so I feel strongly that the standard should be higher.
The system would have to entirely be reformed for me to support it. The standard for evidence should be incontrovertible, bordering on essentially audio-visual proof of the crime or a straight-up confession, or perhaps even both, with the usual assignment of evidence for a standard criminal trial. This evidence needs to be at a level that there isn't just the burden of proof leaning guilty, but rather an incontrovertible and indisputable evidence of guilt. Furthermore, I would remove the ability of lawyers to constantly and endlessly spam the judicial system with appeal after appeal. There can be one appeal, and that is it. There should also be a hard-cap on when the execution must take place. I would say that anywhere between six months to a year of initial sentencing would be adequate.
On the method of execution, I would say that we have gone too far trying to make things "humane" (see: less unpleasant to watch/more clinical and cold in feeling) and return to simplicity. A good hangman will kill a man as quickly and as surely, probably even more quicker and more surer, than a needle. I do not agree with using the firing squad, as that should be reserved for soldiers and more "honorable" forms of execution. Common criminals should be hanged until death.
I would also, in addition to these, return this to a public spectacle. Each district or state or whatever you'd like would have a designated execution location, where condemned criminals will be taken to be hanged. Partially for the sheer retributive justice of it, partially for the example it will set, and partially to sate and redirect the natural tendency of human bloodlust.