In practice, this is just adding 1d10 "damage" to eldritch blast
The trouble with this invocation, as I see it, is that it is a free mini sleep spell, and the problem with that is that, unless you are fighting a horde of minions with really low HP, sleep is more often (in my experience) used to put an injured enemy to sleep, whose HP you think is probably below the average of 5d8, thereby taking them out of the fight.
If you can do this for free, then instead of blasting someone for 1d10, you will instead blast them for 2d10 (if you think their HP is low enough that it'll work) and hope that it puts them to sleep. This gets even worse if you manage to land a critical hit, since now that's 4d10, against one enemy, at which point this is outpacing the sleep spell (of course, you still have to roll that critical hit, but the chance is there, unlike with the sleep spell).
Unless they have friends to wake them up, this puts them out of the fight, which means you can just crit them after the fight (since the fight likely won't last more than a few rounds after this point), or even during the fight, to take them down to 0 HP. Even if they are woken up by allies, or they wake up a few rounds later and you're still fighting, you can just do it again next turn.
Just to make that more explicit; the reason I said above "this is just adding 1d10 "damage" to eldritch blast" is because with 2d10, you have a higher chance of taking someone out of the fight that the 1d10 from using eldritch blast "normally". The fact that they are asleep rather than dead doesn't matter that much, especially as you can just cast it each turn to keep them out of the fight.
This only gets worse at higher levels. Although it's not an area of effect like sleep, it can target creatures individually, which means if you roll low on the first beam and don't send creature #1 to sleep, you can just try again, either at the same creature or a different one, and the poor roll on the previous beam doesn't affect the next beam's rolls, whereas sleep has to share from the same pool. With Agonizing Blast, each beam is dealing between 7 and 25 points of "sleep" damage (assuming CHA of 20), across four beams once we're into Tier 4.
Therefore, at higher levels, this could potentially have a better chance of putting more creatures to sleep than the sleep spell (although it possibly can't compete with an upcast sleep spell, but upcasting sleep just makes it more expensive, whereas this is a cantrip we're comparing it to).
Furthermore, is it intended to affect all beams of eldritch blast at higher levels, or can you switch between "normal blasts" and "sleep blasts"? For example, a high level warlock going "blast, blast, blast, sleep" for 3d10+15 damage, then a sleep effect on the weakened enemy, would be a pretty strong combo for one action that costs them no resources.