I think that many of these avenues converge on one another at different points. Yet, I think that the moral argument can be highly persuasive depending on how it is advanced. The idea of killing being morally wrong and an absolute, regardless of whether an individual or a state does it could be quite effective in going against capital punishment. At the same time, I think being able to argue that the moral and ethical standard of justice is not achieved when murder or execution is the natural end, and that this is actually vengeance could also hold some level of sway. In this argument is the idea that human beings cannot play the divine role in determining who lives and who dies. Finally, I think that advancing the argument that state sanctioned murder does not solve the moral deficit that the original crime had caused. One does not solve ethical bankruptcy by going further in debt. This might be a very persuasive and sound argument against the death penalty.
Agreed with the above answer. Other points to consider. not my opinions necessarily, but arguments that might work:
Socially - Juries are required to sentence a person to death, as are judges. Executioners have to push the button and kill people. A civilized government should not require those in its service to carry out executions.
Morally - the obvious argument is that taking a human life is wrong in any situation, and a government that kills its citizens is committing the moral equivalent of murder. It's the "You murdered someone so we are going to murder you" argument. It's a contradiction.
Constitutionally - I could use the 14th amendment - due process and equal protection under the law for all citizens - to argue that, as pohnpei points out, people do not receive equal legal defenses. Until recently, the mentally impaired could be executed in Texas. In some states you cannot be executed at all. My argument would be that it is impossible to apply the death penalty in a way that meets the 14th amendment, regardless of method.
Historically - The death penalty has only been illegal in this country for 4 years - from 1972 - 1976. Other than that, we have always had a death penalty, with no evidence whatsoever that it is beneficial to either justice or society besides the fact we get to take revenge.
I think that of these four angles of argument, the weakest would be constitutional if you are trying to argue against capital punishment. If you use the constitutional angle, you must prove that capital punishment is cruel and unusual, which would in my opinion be hard to do.
Socially, you can argue that the death penalty does not do anything to deter serious crime.
Morally, you can argue that criminals without money for good lawyers are the ones who get executed. You can also point out how subjective the process of deciding who gets executed is -- one reason why blacks who kill whites get the death penalty more than anyone else.
Historically, you can argue that the practice has been gradually dying out in all Western countries.