Rome has factional slingers until the Marian reforms (where they're replaced by scorpions and auxiliary archers). Also, you can hire Nuraghi Archer-Spearmen on Sardinia, Celtic Archer-Spearmen and Celtic Slingers in Northern Italy and Hellenic archers (bad) and Hellenic slingers (great) in Kalabria and Sicily.
Quite apart from Kretan and Balearic mercenaries being available in the region. Also, try out the recruitable Kretan Archers.
Carthage can recruit Numidian archers and slingers as auxiliaries.
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