/u/kookingpot has a nice view of the secondary and primary sources in this earlier answer:
The practice of infant sacrifice is mentioned by numerous Roman anti-Carthage and Christian anti-pagan authors from antiquity. Thus, for a variety of reasons, people have often felt more comfortable denouncing the claims as propaganda. But archaeology is here to afflict the comfortable. Excavations at the major Carthaginian tophet--a sacred cemetery and ritual site--revealed an entire section dedicated to infant burials. But not just any infants: recent researchers have concluded that the vast majority of infants were healthy and around two months old when they died. For illness, accident, and stillbirth reasons, generalized high levels of infant mortality would be more likely to produce a higher proportion of infants who had died at a younger age (later premodern statistics back this up). Additionally, chronologically the burials themselves are clustered around a distinct moments in time rather than consistently spaced out. This suggests: (1) yes, the infants were probably sacrificed and buried at the sacred site, and (2) it wasn't necessarily a standard or regularly scheduled practice, but a last-ditch, utterly desperate attempt to make things right with the gods in times of calamity and cataclysm.
And you might also be interested in the thread in this post, starring /u/QuickSpore:
Others have already covered the salient physical evidence with regard to infant sacrifice, but I wanted to touch on something briefly on the propaganda part of your question.
It's worth noting, as mentioned by /u/yodatsracist, that human sacrifice wasn't particularly uncommon in the region, up to and including child sacrifice. While the Hebrews certainly took issue with the practice, the Romans were not so hard and fast. Despite repeated 'bans' of human sacrifice, in times of distress, the Romans seem to have resorted to it in an effort to placate the anger of the gods.
Plutarch, Pliny, and Livy all describe human sacrifice by the Romans in times of crisis, like after Cannae and again during the war with the Cimbri and Teutones. In the related question of Gallic practices of human sacrifice, Adrian Goldsworthy cites the latter incident as potential support for the notion that Caesar isn't making it up when he describes it in his Commentaries. That is to say, while the Romans were squeamish regarding human sacrifice, they weren't so squeamish as to totally avoid it if the situation were bad enough.
And in that light, accusations by the Romans of human sacrifice by the Gauls, Germans, Carthaginians, and so on might be better understood not as purely fictive inventions, and perhaps instead as commentary on each society's respective attitudes towards it.
Sources:
Goldsworthy, Adrian, Caesar: Life of a Colossus
Livy, A History of Rome
Plutarch, Life of Marcellus
Pliny, Natural History
Edit: just tidying up my language