For anyone who cannot access the link I referred to earlier, the following is the config file I created to allow the Mupen64 core to work with a real N64 controller connected via the 4-Play. Note that this config is valid for up to 4 players.
###############################################################################
# RetroArch input mapping file for using real N64 controllers in
# Mupen64Plus with a BlissBox 4-Play adapter.
#
# The default input mapping for the Mupen64 core assumes the player is using
# an XBOX or PS Dualshock-style controller. Because these controllers do not
# have enough face buttons to emulate the N64 C-buttons in addition to A & B,
# the core provides 2 ways to send C-button input:
# 1) Retropad right analog stick
# 2) Retropad Y => C-Left, X => C-Up
# Holding R2 overrides Retropad A & B to map B => C-Down and A => C-Right
#
# When attempting to use a real N64 controller, the R2 button override
# functionality isn't needed. In fact, it greatly confuses the configuration.
# There are also a few additional tweaks required to improve usability.
# So this input file overrides the 'default' 4-Play input assignments
# settings to support a real N64 controller layout without any additional
# remapping at the RA core level.
#
# Consider 'default' 4-Play input settings to be those set by
# retroarch-joyconfig when using a BlissBox 4-Play with a PS2-DualShock
# controller. The following changes were applied to that config to make
# everything play nicely together:
#
# 1) Limited C-Button input to only the right analog stick by disabling the
# the Retropad buttons that are normally mapped to C-button functions:
# - Retropad inputs X, Y, and R2 mapped to "nul"
# 2) Assign Retropad's right-analog inputs to the 4-Play's N64
# C-button assignments:
# - Remove the default Retropad right analog inputs by
# mapping to "nul"
# - Assign Retropad right analog inputs to the real N64
# C-button inputs
# 3) Swap the position of the A & B buttons to match the real N64 layout
# 4) Z-Trigger assignment changed from 4-Play's SELECT to L2
# 5) Disable remaining buttons that don't exist on a real N64 controller:
# - Retropad inputs SELECT, L3, R3 mapped to "nul"
#
# In order to effectively use this configuration, you should NOT have any
# core input remapping files enabled. Check the following settings:
# auto_remaps_enable = "false"
# input_remap_binds_enable = "false"
# input_remapping_path = ""
#
# These settings can be applied by merging them into your retroarch.cfg
# file, or the per-core config if applicable. If you do this, you need to
# disable the joypad autoconfig functionality, since the autoconfig settings
# are higher priority and will override settings included in the master
# .cfg file. You can disable the autoconfig by changing the following
# setting:
# input_autodetect_enable = "false"
#
# This config can also be applied through the core-specific configs. Simply
# add these settings to "<RA_Config_Dir>\Mupen64Plus\Mupen64Plus.cfg". RA
# will automatically look for this file and override the main .cfg settings
# with anything in there. If you use this method, you still need to disable
# the joypad autoconfig settings as mentioned above.
#
# The final method for applying these settings is to use the append config
# functionality from the command line: "--appendconfig file1.cfg,file2.cfg"
# Just pass the file containing these settings to that option. If you use
# this approach, you DO NOT need to disable the joypad autoconfig. The
# appendconfig setting has the highest precendece, and will override all
# other configuration settings used by RetroArch.
###############################################################################
input_player1_b_btn = "0"
input_player1_y_btn = "nul"
input_player1_select_btn = "nul"
input_player1_start_btn = "5"
input_player1_up_btn = "10"
input_player1_down_btn = "11"
input_player1_left_btn = "12"
input_player1_right_btn = "13"
input_player1_a_btn = "1"
input_player1_x_btn = "nul"
input_player1_l_btn = "6"
input_player1_r_btn = "7"
input_player1_l2_btn = "4"
input_player1_r2_btn = "nul"
input_player1_l3_btn = "nul"
input_player1_r3_btn = "nul"
input_player1_l_x_plus_axis = "+0"
input_player1_l_x_minus_axis = "-0"
input_player1_l_y_plus_axis = "+1"
input_player1_l_y_minus_axis = "-1"
input_player1_r_x_plus_btn = "9"
input_player1_r_x_minus_btn = "2"
input_player1_r_y_plus_btn = "8"
input_player1_r_y_minus_btn = "3"
input_player1_r_x_plus_axis = "nul"
input_player1_r_x_minus_axis = "nul"
input_player1_r_y_plus_axis = "nul"
input_player1_r_y_minus_axis = "nul"
input_player2_b_btn = "0"
input_player2_y_btn = "nul"
input_player2_select_btn = "nul"
input_player2_start_btn = "5"
input_player2_up_btn = "10"
input_player2_down_btn = "11"
input_player2_left_btn = "12"
input_player2_right_btn = "13"
input_player2_a_btn = "1"
input_player2_x_btn = "nul"
input_player2_l_btn = "6"
input_player2_r_btn = "7"
input_player2_l2_btn = "4"
input_player2_r2_btn = "nul"
input_player2_l3_btn = "nul"
input_player2_r3_btn = "nul"
input_player2_l_x_plus_axis = "+0"
input_player2_l_x_minus_axis = "-0"
input_player2_l_y_plus_axis = "+1"
input_player2_l_y_minus_axis = "-1"
input_player2_r_x_plus_btn = "9"
input_player2_r_x_minus_btn = "2"
input_player2_r_y_plus_btn = "8"
input_player2_r_y_minus_btn = "3"
input_player2_r_x_plus_axis = "nul"
input_player2_r_x_minus_axis = "nul"
input_player2_r_y_plus_axis = "nul"
input_player2_r_y_minus_axis = "nul"
input_player3_b_btn = "0"
input_player3_y_btn = "nul"
input_player3_select_btn = "nul"
input_player3_start_btn = "5"
input_player3_up_btn = "10"
input_player3_down_btn = "11"
input_player3_left_btn = "12"
input_player3_right_btn = "13"
input_player3_a_btn = "1"
input_player3_x_btn = "nul"
input_player3_l_btn = "6"
input_player3_r_btn = "7"
input_player3_l2_btn = "4"
input_player3_r2_btn = "nul"
input_player3_l3_btn = "nul"
input_player3_r3_btn = "nul"
input_player3_l_x_plus_axis = "+0"
input_player3_l_x_minus_axis = "-0"
input_player3_l_y_plus_axis = "+1"
input_player3_l_y_minus_axis = "-1"
input_player3_r_x_plus_btn = "9"
input_player3_r_x_minus_btn = "2"
input_player3_r_y_plus_btn = "8"
input_player3_r_y_minus_btn = "3"
input_player3_r_x_plus_axis = "nul"
input_player3_r_x_minus_axis = "nul"
input_player3_r_y_plus_axis = "nul"
input_player3_r_y_minus_axis = "nul"
input_player4_b_btn = "0"
input_player4_y_btn = "nul"
input_player4_select_btn = "nul"
input_player4_start_btn = "5"
input_player4_up_btn = "10"
input_player4_down_btn = "11"
input_player4_left_btn = "12"
input_player4_right_btn = "13"
input_player4_a_btn = "1"
input_player4_x_btn = "nul"
input_player4_l_btn = "6"
input_player4_r_btn = "7"
input_player4_l2_btn = "4"
input_player4_r2_btn = "nul"
input_player4_l3_btn = "nul"
input_player4_r3_btn = "nul"
input_player4_l_x_plus_axis = "+0"
input_player4_l_x_minus_axis = "-0"
input_player4_l_y_plus_axis = "+1"
input_player4_l_y_minus_axis = "-1"
input_player4_r_x_plus_btn = "9"
input_player4_r_x_minus_btn = "2"
input_player4_r_y_plus_btn = "8"
input_player4_r_y_minus_btn = "3"
input_player4_r_x_plus_axis = "nul"
input_player4_r_x_minus_axis = "nul"
input_player4_r_y_plus_axis = "nul"
input_player4_r_y_minus_axis = "nul"