SAE 20 I believe is recommended.
Here's what guru Sheldon Brown has to say:
Lubrication
Only thin good quality oil should be used for the lubrication of Sturmey-Archer hubs. (Phil Wood Tenacious Oil is my favorite for this application --SCB) (Automotive automatic transmission fluid also is good, and inexpensive -- John Allen). Thick oils or grease must not be used, but when a hub is dismantled a small amount of grease or vaseline may be put on the ball races only. (Note that this information contradicts other information from Sturmey-Archer, to put grease only on the labyrinth seals. The point of this advice is to keep grease away from the pawls -- John Allen)
The ideal rule for lubrication should be 'a little but often'. Two or three drops of oil every week will maintain the hub in first class running order. A new hub should always be oiled before use because the oil put in at the factory may have evaporated in the interval between leaving the factory and being put to use on the road.
TCW (Tricoaster) hubs need more oil than other hubs because in their case the oil is used not only for lubrication but also to dissipate heat generated by the brake. (that is, the oil burns up -- John Allen).