I shoot Lee-Enfield .22 milsurp rifles so am in the same boat, as these rarely take beyond low supersonics at all well (my current favourite rifle is a 1915 trainer which has probably had millions of rounds through it, and has some unhappy throat erosion - but still a joy to shoot if you stay under 40 yds and are happy with a two inch group!).
I've tried pretty well everything subsonic around and agree that CCI standard is probably as good as you're going to get, and widely available. Remington subsonics are OK but are relatively underpowered, I think about 1050 fps as opposed to about 1080 for the CCIs. Another 1080ish is the Federal Gold Star 711B, I think (there are two Federal Gold Stars, and be careful to get the subsonic one!). Currently I'm shooting Eley ammunition out of my v accurate Lee Enfield C no 7. It's British target ammo sold here by Remington and comes in three or four grades, from cheap target to expensive match grade (about equal to the green tag CCI), all about 1080 fps. The smell is an acquired taste if you're used to American made 22 ammo!
Some of the faster subs can go super in the right humidity/temp, so beware the occasional crack and wear ear protection. I think I've only had this happen regularly with the Federal Gold Star.