from what my sources tell me (that sounds fishy doesnt it :P) the color dreams mapper works like this:
Bit 0: controls A15 of PRG
Bit 1: not used
Bit 2: Lockout circuit control
Bit 3: Lockout circuit control
Bit 4: controls A13 of CHR
Bit 5: controls A14 of CHR
Bit 6: controls A15 of CHR
Bit 7: not used

to make a write to the 74LS377 (since the PRG's RW and Ce need to be enable), you would need to have a table with the values you would want to write to and save that value to a ROM location with that value.

for example, to write 01111101 to the 377, you would do something like this

;##########################
lda #$7D
sta TableThing

TableThing:
.db $7D
;##########################