I would have my own cavalry archers to start with. But if your the romans and cant train any then either let them waste their arrows and javelins on your superior armour and then engage for the melee.
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Use your own long range archers. Keep some in reserve to use against the missile cavalry and they will slaughter the them.

Elephants are always usefu in fighting skirmishers as well.

Its not too hard, I managed to surround some parthian horse archers with armoured hoplites once, once you zero in on them you cant really lose.

Archers. Slingers. Mounted archers. Run them down with cavalry.

Run them down with cavalry!

You can try tactics to get them to engage one (or more) non-cav (or even cav) units, then hit with cavalry from another direction.

However, often you can't avoid "the chase", which is a pain if you want to avoid nagging injuries & deaths of your own troops in the process. The best way to describe how I handle mobile skirms (incl. eastern, not just Numidia) is like a Texas cattle drive. I "herd" them with my Equites (or light cav, if using a non-Roman civ). I click on the far edge of the map, parrallel to the direction of flight, and do not try to engage units of similar speed, then I make "cuts" (quick change of direction, momentarily, toward the unit, even if I cannot get to grips) to 'steer' them to a map edge. Units, even infantry, can be used to converge to the expected point of battle from near or far, all you need to do is mentally compute the correct intercept vector, given the speed differential, to know where they will meet (I try to make that point on a map edge to avoid continued enemy flight). Once a unit (of mine) strongly engages the enemy being herded, they will be forced to stop flight, and fight. If it is an Equite unit that is engaging a more powerful (numeric or quality), like an eastern general (or FL), then you better have good timing with more units, esp. your slower General unit(s) or infantry, or else...

Naturally, it takes time and micromanagement to hunt down mobile skirmishing units, and since I personally rarely have battlefield numerical superority (except at the end of the battle), I have to prioritize when my cav units can be turned loose on 'the cattle drive.' Sometimes, they must fight at the main lines under fire in order to ensure the rout of enemy infantry, for instance.

The guiding method for making these decisions, for me, is experience (e.g., often a gut guess) of knowing whether I will take more overall casualties by routing the main enemy battle line whilst being pelted, then dealing with the skirms, or visa versa. It is also a consideration where on the battlefield the main line is, and likely direction of flight of routed enemy (can I hunt down some skirms, and still turn to hunt down the routed enemies before they can exit the battlefield?).

Literally, Good hunting...

Ya, they are annoying, I recall one battle that resulted in me chasing the enemy around for at least 20 mins while they followed the border line of the battlefield. I was Greece so didn't have much cavalry and they were, I think, egypt with some chariots. I eventually beat them by putting out some militia cavalry. I had turned off the skirmish button and the chariots were about 5 feet away from the cavalry (they had run out of arrows and decided to charge)when my horse hurled their javelins point blank and routed the already nervous enemy.

I never liked facing numidia, first time I did I was shocked. Those desert infintries were much stronger then eastern infintry. But yes with all there base on run/ride and throw they can be quite tough, but just get some slingers.

I have played - and beaten - the game on VH/VH as Carthage. Carthage has an advantage over Numidia in pure strength, but the Numidians are much faster, because they have less armor.

As previously said, cavalry are excellent to stop harrassing skirmishers. The downside - if you don't have as many cavalry units as they do skirmishers, you risk either routing your cavalry units or having them killed outright. However, the AI for units in skirmish mode is severely flawed - if you know how to expose it.

Run your cavalry units behind the enemy skirmishers. Then send them to attack the skirmishers from behind. If you line up your infantry correctly, the skirmishing units will flee away from the advancing cavalry units as fast as possible - and the fastest way away from them is the same direction as them. So if you can get them to run straight into your lines of infantry, their skirmishers aren't going to harrass anyone ever again.

Keep in mind, your opponent will have (most likely) infantry and cavalry to back their skirmishers up, so keep an eye on the map to see what your enemy is up to.