Mal, a lot of the dates I can find seem to be for jump-1 discovery. I've had a look through for jump dates. This is what I've been able to glean from the resources I have to hand. Check out
The Traveller Timeline for referenced timeline information.
Vilani
jump-1 -9235 (MT Imperial Encylopedia)
jump-2 -5430 (MT Imperial Encylopedia)
developed before the Consolidation Wars
Aslan
jump-1 -1999 (MT Imperial Encylopedia)
jump-5 -1014 (Alien Module 1 - Aslan)
discovery of jump-5 route so presume they have the capability
Solomani
jump-1 -2431 (MT Imperial Encylopedia)
jump-2 -2398 (GT: Interstellar Wars)
jump-3 -2285 (GT: Rim of Fire)
GT: Interstellar Wars also has reference to the jump-3 being developed during 8th IW and used in the 9th IW. Dated at -2280 in Supplement 11 - Library N-Z - GDW.
Darrian
jump-1 -1395 (GT: Humaniti)
jump-2 -1370 (Alien Module 8 - Darrians)
jump-3 -1370 (Alien Module 8 - Darrians)
reference of jump-2 ships in use with some jump-3