I agree, but make them public. But LN2 is acceptable also.
No to firing squads.
They have a certain amount of romanticism attached to them.
No head-chopping, thank you. Leave that to the French who showed how out of control they were, and the Moslems.
Gallows are the best. Break a neck fast, cheap. Public viewings should be brought back, too. That helps with the deterrent effect.
I disagree with all those as well as any the state uses, whether gas, electricity, drugs, etc. Instead the right form is that which was used in Scripture, that being (usually) stoning, versus letting another to the dirty work .
I think this fostered a more fitting, deeper, sober and sense of responsibility. For the sin was not only against one but to varying degrees it was against the community, who thus should be able to engage in the retribution.
And knowing that the community would actually do the killing would have a greater deterrent against false testimony, as a liar would fear the wrath of the people he involved in his crime if he was found out.
Also, taking part in stoning one to death would also impress upon the people the gravity of the crime, and give them a sense of justice, more so that the state taking the guilty away for private execution.
And which in turn places greater appreciation on mercy, seen in contrast to justice.
The best and most effective method would be to put the perp in an airtight chamber, then remove the air. The perp would even enjoy it as it causes euphoria. It takes very little time also. Give the perp a 6 pack and s/he probably won’t finish the first beer.