Types of argon gas regulator?
No cylinder regulator that I know of will provide fine control of flow rates on the order you require.  The purpose of a regulator is to control the line pressure, not the line flow rate.  In theory you could stick a flowmeter in-line and try to finesse the regulator pressure and shutoff valve (if there even is one) to reach the flow you want, but it would probably be a maddening exercise.

What you need is a mass flow controller (MFC) of some kind.  Depending on your budget and your needs for adjustability and precision of the flow rate, there is a variety of options:


If you know you will only require a specific, set flow rate (or, a small number of set flow rates) you might do okay with a flow orifice: set the upstream pressure appropriately and the flow should match the spec.
If you need to be able to vary the flow rate and an approximate value is acceptable, something like these dial-knob flow control valves would probably work okay.
If you need precise control of the flow rate, you're probably up against something like these Porter mass flow controllers. They're quite pricey (a few thousand USD) but they work extremely well.  You'd need both the in-line MFC unit and the separate control box to make it work.


IMPORTANT: One thing to be aware of is that all of these technologies are gas-specific to a greater or lesser extent.  The orifices and dial-knob controllers depend at least on the viscosity and density of the gas, and the Porter MFCs depend also on the specific heat of the gas.  The differences will be minor, so I wouldn't worry about it for the first two, but if you need highly precise flow rates, you will have to compensate for the differences if you should need to switch gases.  Porter actually calibrates each MFC to a specific gas, so if you only need argon flows, you'll be all set.