Error Analysis due to Voltmeter Constraints
I don't own a Keithly 2182A so I can't verify this answer, but I think the command sequence shown below in Listing 1 should be a good starting point for your program. Of course, you will need to reconfigure some of the settings to meet your requirements.

See also the User's Manual for the Keithley Model 2182/2182A Nanovoltmeter (document 2182A-900-01 Rev. B / May 2017). This manual is available for download from Tektronix's website (https://www.tek.com).

Listing 1.

// 
// Configure the instrument's settings to a known/default condition
//

*RST
*CLS

//
// Configure input channel 1
//

:SENSe:CHANnel 1
:SENSe:FUNCtion 'VOLTage:DC'
:SENSe:VOLTage:DC:RANGe 10      // Use fixed range for fastest readings.
:SENSe:VOLTage:DC:NPLC 0.01     // Use lowest NPLC setting for fastest readings.
                                // (NPLC := Number of Power Line Cycles)

//
// Configure input channel 2
//

:SENSe:CHANnel 2
:SENSe:FUNCtion 'VOLTage:DC'
:SENSe:VOLTage:DC:RANGe 10      // Use fixed range for fastest readings.
:SENSe:VOLTage:DC:NPLC 0.01     // Use lowest NPLC setting for fastest readings.

//
// Disable instrument features that slow down the measurement speed
//

:DISPlay:ENABle OFF             // Turn off display to increase speed.
:SYSTem:AZERo:STATe OFF         // Disable autozero to increase speed, but may cause
                                // drift over time.
:SENSe:VOLTage:DC:LPASs OFF     // Turn off analog filter for speed.
:SENSe:VOLTage:DC:DFILter OFF   // Turn off digital filter for speed.

//
// Trigger a measurement cycle
//
// NB: *RST disables continuous trigger initiation
// :INITiate:CONTinuous OFF
//
// NB: *RST sets the trigger count to 1 (one)
// :TRIGger:COUNt 1
//

:ABORT                          // Reset the trigger system
:INITiate:IMMediate 1           // Trigger one measurement

//
// Code that waits for the triggered measurement to finish
// do {
//    sleep 100 ms              // Sip some coffee
//    *STB?                     // Query the instrument's status byte
//    (enter status, store status in variable STB_VALUE)
// } while ( MEASUREMENT AVAILABLE (MAV) bit is not set in STB_VALUE );
//

//
// Fetch the measurement data
//

:FETCH?
(Enter readings)

//
// Re-enable the previously disabled instrument features
//

:DISPlay:ENABle ON              // Turn on display.
:SYSTem:AZERo:STATe ON          // Turn on autozero.
:SENSe:VOLTage:DC:LPASs ON      // Turn on analog filter.
:SENSe:VOLTage:DC:DFILter ON    // Turn on digital filter.