Build is a rogue assassin/hexblade(5)/bard(2) (or bard 1/sorcerer 1) , has elven accuracy, is dual wielding a shortsword (vex) and scimitar (nick, scimitar is the pact weapon), and has thirsting blade and eldritch smite as the warlock 5 invocations, so if the character goes before his target in round 1 he has advantage on all 3 attacks, his bonus action will be using hexblade's curse so will rolling a total of 9 d20's for 3 attacks and critting on a 19 or 20, and burning a 3rd level pact magic to eldritch smite the first 2 times he crits a significant opponent.   If i.can keep advantage I'll get the 9 d20 rolls each round making at least 1 crit a round fairly likely.   If I don't have advantage, I could attack with short sword (vex) first, if I hit it'll grant advantage on the next attack, otherwise burn a lucky, then sneak attack, use a d6 for trip/prone and the third attack has advantage.  Which brings me down 7 d20 rolls a round.  Once i have bard 1 Ill be able to Faerie fire twice  a day (or use silvery barbs, to make an opponent fail a save and grant myself an advantage on my next attack) but if I was able to keep the opponent from getting up, I'll get the 9 rolls a round without spending resources.

So how could I keep a prone opponent from getting up (apart from reducing him to zero hp or grappling him)?

Anything that applies the Restrained condition is your friend here, since a Restrained creature has a speed of 0, and you can't stand up if your speed is 0.

Become proficient in improvised weapons, and use a net as a weapon for one of the weapons. And have a steady supply of nets.

Grapple.

Any effect that make your speed 0 will do, such as the Grappled, Paralyzed, Petrified, Restrained or Unconscious condition.