David Meadows has blogged the main evidence and points out the obvious (but too often ignored point) - when is a Tophet a Tophet, and when is it a child cemetery? His post is really worth reading and can be found here: Child Sacrifice at Carthage?
My view is that it's clear from ancient sources that the Carthaginians followed the Phoenicians and sacrificed humans. The extent to which they did this, and when they stopped, is unclear - but what I read into Diodorus Siculus says (20.14) is that the practise had not lapsed prior to Agathocles' invasion, but that the Carthaginians had been substituting others (foreign slaves) rather than sacrificing the sons of the elite:
They also alleged that Cronus had turned against them because, whilst in former times they had been accustomed to sacrifice to this god the noblest of their sons, more recently, they had been secretly buying and raising children, and they had instead sent these to the sacrifice; and when an investigation was made, some of those who had been sacrificed were discovered to have been fraudulently substituted.The Romans sacrifices humans as officially sanctioned acts of state until the very end of the second century BC. In the early first century BC human sacrifice was outlawed, and we know of no more state-sanctioned human sacrifices - though private ones continued into the early Christian period. Earlier, human sacrifices had been considered by the Greeks before Salamis. To claim that the ancients were 'just like us' and didn't do these horrible things is naive - and attempting to re-write history.