Healing: Psychometabolism powers of the healing subdiscipline can remove damage from creatures. However, psionic healing usually falls short of divine magical healing, in direct comparisons.
Doing a quick pdf search for healing, it seems most of the powers are psychometabolic and only have a range of "personal." The ones that do work on others don't heal hp damage, they just restore ability damage, regrow limbs, etc. The revivify power's text states that it acts just like a raise dead, and none of the exceptions seem to counteract the idea that it would affect undead the way the spell would do so.
However, that said, there's nothing about positive energy anywhere. This is more mind-over-matter type stuff. If you had an undead psionic creature, it should be able to use its own psionic abilities to heal.
The Vitalist can use their Collective ability to use Personal powers like that on others inside the Collective. But yeah, psionic healing appears to be untyped unless specified otherwise.
I would think that if you went to that great an effort, yes you'd manage to harm the undead.
Bards get some cure spells as arcane spells, so it's not even necessarily that divine sources are needed to harm undead.
That said, what happens if you stick a ring of regeneration on an undead? It gains a hit point every round. The ring just heals the wearer because that's what it says it does. Amusingly the regenerate spell only works on living creatures. Huh.
So, really, this comes down to DM fiat though I know I'd rule that psychometabolism can harm undead.