Page about the INA219 : INA219 data sheet, product information and support | TI.com
The Adafruit library seems to be not suited for the lowest current range.
The "ina219_currentDivider_mA" variable is an integer, which should be set to 25/8 for the lowest range (I think). So you might have to write your own interface.
The "ina219.begin()" is the "Adafruit_INA219::begin()" in the "Adafruit_INA219.cpp" file.
It calls a function "ina219SetCalibration_32V_2A()".
That function sets the config register in the INA219.
There is also a function "ina219SetCalibration_32V_1A" which you could use, instead of the '2A' version.
The '1A' version can be altered, but a mistake is easy to make.
In "Adafruit_INA219.h", the define "INA219_CONFIG_GAIN_1_40MV" will set the highest precision.
You could do this:
Make the "ina219_currentDivider_mA" a float in "Adafruit_INA219.h".
Rename "ina219SetCalibration_32V_1A" to "my_ina219SetCalibration"
Call that function from "Adafruit_INA219::begin".
Replace in "my_ina219SetCalibration" the define "INA219_CONFIG_GAIN_8_320MV" by "INA219_CONFIG_GAIN_1_40MV"
Adjust the values for "ina219_currentDivider_mA" and "ina219_powerDivider_mW" by dividing them by 8 in that function.
So it is not easy to do.
You could check the forums at Adafruit.
Or use a different library. I like this one : http://www.johngineer.com/blog/?p=1178
In his README file, John De Cristofaro writes this: "Something to keep in mind however, is that this change in gain DOES NOT affect the resolution of the ADC, which is fixed at 1uV."
So after all, I would suggest to use the Adafruit "1A" function as it is.