You are asking here about “other” types of punishment, but we do not know what types you have already identified. Therefore, we cannot be sure which punishments are “other.” I will, therefore, assume that you are asking about punishments other than those that are typically used in the United States today.
If that is the case, the answer will vary a great deal depending on what kind of crime you are talking about. People will probably accept different punishments for different crimes. For example, it seems likely that most Americans today would accept lighter sentences for non-violent drug crimes. They would probably accept punishments that did not involve prison because they are tired of paying huge amounts to incarcerate people who are not much of a threat to most of society. On the other hand, many Americans would probably accept much more draconian punishments for sex offenders. “Chemical castration” would probably be accepted more widely than it already is in the cases of the worst child molesters and rapists. As for crimes against property, I imagine that most Americans would accept more punishments that would be centered around making things up to the victim. Punishments that involved restitution and being made to work in ways that will benefit the victim would probably be acceptable to most Americans.