The Western Phoenicians have only few native troops availible to them at one given time. These are Independant of City politics but change with unlocking certain Skills.

(these are all Type-Names, ingame they have native names which will change once I get that dictionary int he Mail)

Phase 1 - Levantine Settlers with Equipment of assyrian Style
- Syrian Spearmen (basic Spearmen) - Replaced in Phase 2
- Syrian Cavalry (Long Range Cavalry) - Replaced in Phase 2
- Syrian Guard (Hardy heavy Infantry) - Replaced in Phase 2
- Levantine Infantry (Archers) - Replaced in Phase 4
- Phoenician Sailors (naval Archers)

Phase 2 - Greek Imports (Greek wares Skill)
- Punic Heavy Infantry(Hoplites) - Replaced in Phase 3
- Punic Citizen Cavalry(medium Cavalry)
- Sacred Band Infantry(heavy Hoplites) - Replaced in Phase 3 - also requires a Temple
- Phoenician Marines (Javelin infantry)

Phase 3 - Mercenary Contractors (Social Reform)
- Libyan Skirmisher(javelineer)
- Libyan Spearmen(medium Infantry)
- Punic Militia (light Hoplites)

Phase 4 - Lords of the West (military Reforms)
- Libyphoenician Cavalry(heavy Cavalry) - also requires Colonization
- African Elite Infantry (Heavy Infantry) - also requires Colonization
- Elephants (Elephants, nuf said!) - also requires an Elephant Port

Not all Reforms Improve your Roster, for example Syrian Cavalry is a lot better than Punic Citizen Cavalry and Punic Milita is no match for Punic Heavy Infantry. So don't rush those Skillresearches. Also keep in mind that many Punic Troops can only be trained in Coastal cities.
However that's only one side of the story, on the other are all the extra Mercenaries Punics have access to and the availibility of Embassies in conquered cities, that provide you with a wide selection of local troops. Embassies can even be further upraded with the right Skill research(in the Military Tree), en route increacing the amount of mercenaries availible in EVERY town you controll.