The archaeological evidence confirms that they did, in fact, sacrifice children. There was a special area known as the Tophet which contained cremated human and animal remains, and many of these were children or infants. These remains were found in proximity to a large amount of ash from burned olive wood, and thus the remains have been interpreted as being the results of sacrificial offerings. There's also all the Roman descriptions of Carthaginians sacrificing children, which could be interpreted as propaganda, but there's a bit more to it.

As a matter of fact, Tophets have been found across the Carthaginian world, from Sardinia to Spain, but the word itself refers to a site near Jerusalem in which the act of child sacrifice was said to occur in the Bible, and the word is in fact Hebrew, not Punic (though the two languages were very closely related). This evidence, in fact, is helpful in determining what the Tophet of Sallambo (the one next to Carthage) was for. The Bible describes ancient Canaanite religion as having included child sacrifice, and as both the Carthaginian and Israelite religions developed out of Canaanite religion, it stands to reason that they would have evolved attitudes to it. One continued the practice, and one seems to have repudiated it.

There's even a theory that the Binding of Isaac story in the Bible is about child sacrifice. One theory is the stories is actually two stuck together, one in which Isaac was actually sacrificed, and one in which he was replaced by a ram. The second story would have been a repudiation of and replacement for the first.