Nids and Daemons are both relatively good matchups against Harelequins.
Harlequins are an army of no armour saves but army-wide invulnerable saves and so laugh at armies relying on low-
AP firepower. Nids have very little of that but are excellent at just piling on wounds and forcing saves. Not great against 2+ armour saves, but it works well when the highest save in the army (one model, the Solitare, not included) is a 5+, invulnerable or no. Nids also have a lot of S6 knocking around, most notably brainleech devourers and the Mawloc's S6 Deep Strike blast. This will
ID the Shadowseer, Death Jester and Troupe Master characters that form a big part of the Harlequin army, as well as make mincemeat of their light transports (there's no AV14 to worry about here). Speaking of Flyrants, Harlequins have very little that can deal with fliers and so a couple of Flyrants will prove very hard for your friend to deal with.
Daemons sort of flip the first point I made around as their own army-wide invulnerable saves help mitigate the Harlequins' ability to heap a lot of AP2 on you in combat. Sadly,
CSM, as with most
MEQs, will get hit hard by this. I'm not very familiar with Daemons, but, as I understand, they have Fearless (or at least some form of it?), army-wide? One tactic many Harlequin players employ is leadership reducing shenanigans to force Pinning and easily-failed Morale checks where they can catch you with Sweeping Advance easily thanks to I6+ across the board. Bear in mind though that Fearless won't protect you from any Psychic Shrieks their Shadowseers bring to the table, often combined with an item that will reduce your leadership by 2 if you're within 12".
Speaking of Shadowseers, another advantage of Tyranids and Daemons is the ability to go toe-to-toe with Harlequins in the Psychic Phase, which is important considering the numerous nasty spells the Harlequins have access to.
Finally, bear in mind that Harlequins are battle-brothers with both Dark Eldar and Craftworld Eldar and that the three armies are regularly combined. Indeed, Harlequins don't work brilliantly as a stand-alone army (especially in larger value points games) due to the limited options available in their codex and so allies are a common sight, to fill out the points if anything.
Hope this helps, if you have any more questions don't hesitate to ask!