I second salterius suggestion, the key to conquest is not holding the systems for long, but holding them at once, and yes UE's flat -50% overcolonization combined with federation government do very nicely.
So think ahead, set up a "swing turn" in which you'll likely obtain a set of systems at once and close out a conquest victory without running risk of rebellion, as you will not hold them for unnecesarily long, this may also include triggering minor faction quest completion or assimilating them on demand (and first in order).
You can also prepare those less popular systems you skipped before, simply colonize everrything, perform quick maths, and win.

High galaxy density setting helps, conquest requirements are usually more reasonable on smaller map sizes eg. holding 40+ systems on big maps is quite challenging given the penalties.

Good picks would also be cravers for the sake of aggresive conquest and umbral choir for less impeded expansion and more overall control of the swing turn, but also more relying on the swing turn.

To show what a good swing turn looks like, here's a vid of taking over 6 systems in one turn, which has debilitating consequences due to the umbral choir heavy overcolonization malus, but makes no difference as the victory is achieved. 
You can also adapt the "slow and steady" approach, but as conquest is one of those less science involved victories, it can be achieved quite early.