The class 37 loco group website is usually a good source for this sort of thing, but I don't think that even they maintain such a list (link included as an example, though):
http://www.c37lg.co.uk/history.aspx
It can get very complicated if you start to consider all the different permutations of BR blue and the large logo liveries (White stripes, yellow cab sides, large/small BR double arrows, etc).
I'm not aware of such a list anywhere else, either, but here is what I think have been the main livery variants:
BR Green, lion and wheel emblem
BR Green, double arrow logo
BR Blue, double arrow logo
BR Large Logo (Applied to all the 37/4s as they underwent conversion, also carried by a number of 37/0s and 37/3s)
BR Railfreight "large logo" Grey/yellow
BR Railfreight "red stripe" Grey yellow
BR Mainline (Essentially unbranded Intercity "swallow" livery)
Trainload Freight - General (Red and yellow rectangles - Carried only by 37104, 673 and also 403 for one night only)
Trainload Freight - Railfreight Distribution (Red rhombus' on yellow background)
Trainload Coal (Black diamonds on yellow background)
Trainload Construction (Blue and yellow squares)
Trainload Petroleum (Blue and yellow waves)
Trainload Metals (Blue and yellow chevrons)
BR Unbranded trainload freight triple grey
BR Civil Engineers "Dutch" (Grey/yellow)
BR Departmental (All over dark grey)
BR Regional Railways
BR Intercity Swallow (As applied to 37152/221/251/505/510/683/685 for working the Inverness and Aberdeen sleepers with generator vans between 1992 and 1994, since carried by 37518 in preservation)
BR Trainload Freight - Mainline "rolling wheels" branding in blue
Mainline Freight (Aircraft blue with silver decals)
Loadhaul (Black/orange)
Transrail
European Passenger Services (Trainload freight triple grey with the Channel tunnel "polo mint" metal segments)
European Passenger Services - Blue DRS branding (As applied to six class 37/6s at the end of the nineties)
English, Welsh & Scottish Railway (Red/gold)
Royal Scotsman maroon (Different permutations - 37428 initially with large yellow numbers, 37401 and 416 later with small numbers)
Direct Rail Services
GIF (Spain) Light and dark blue
Harry Needle Railway Company Light grey/orange (Worn by 37087/194)
BR Two-tone green (As worn by classes 24, 25 and 47. Only carried by 37197 while owned by Ian Riley)
West Coast Railway Company Maroon
DRS "Compass"
Network Rail Yellow
DB Schenker Red
Colas Rail Orange/Yellow/Black
Europhoenix (Grey, blue and red)
DRS "Swirly compass" (As applied to the new class 68s)
That's everything I can think of, there might well be others that I have missed! Class 37s have been painted in just about everything going, being such a versatile design.
There have also been a number of permutations and one-offs in addition to the mostly standard schemes listed above:
37501 received a British Steel blue livery in the eighties.
37116 "Sister Dora" carried BR blue livery with the Transrail "Big T" logo during the mid to late nineties.
A few locomotives, such as 37350, 403 and 411 have also been returned to BR Green livery at various times from the nineties onwards, to varying levels of authenticity.
Not forgetting the time that 37093 was dressed up in a predominantly white "Police" livery for an IC125 advert in the early eighties!
