Why not be able to but them from other Civs?
Have a way of designating a unit is available as a Mercenary and then have them appear as an option in the Diplomatic screen. Then you could buy them from their original Civ. They could have an upfront gold cost (perhaps a gp cost the same as their production cost modified by the Civs attitude towards you) and then a higher upkeep, x2 or x3. They would then be your unit to control but would not upgradeable (promote as normal) and they would heal at the same rate as units in neutral territory.
Or another idea may be to have tile improvement 'Marshalling Grounds'. It would have to be built in your territory and connected to the trade network that attracted agents for mercenaries, but at random. It does nothing but attract mercenaries.
The mercenaries attracted should be of roughly the same quality as being produced by the Civs you have contact and trade with. Have the chance of appearance of mercenaries linked the the closeness of hostilities as that is where mercenaries are most likely to appear anyway.
For those Civs that want to build up some extra units before starting a war there could be an option at the Marshalling Grounds to hold a Fete or Tattoo or something that indicates they are interested in attracting mercenaries. It should cost a bunch of money but would be more likely to attract mercenaries and of a slightly better grade (but corresponding higher cost and upkeep).