How many milliamps are minimally required for transistor couplers to operate?

It largely depends on the product type and the current transfer ratio the relevant product has. Considering actual applications, products with general performance can be used with a current at the input side in a range of several milliamps, and low-input type (high-sensitivity type) products can be used with one in a range of around 1mA. However, this may change greatly depending on the required response time and load resistance range.
For details, refer to Toshiba Application Note "Basic Characteristics and Application Circuit Design of Transistor Couplers", section 2-4.Design Example for Interface Circuit Using Transistor Coupler.