Melira's Keepers can't have any kind of counters placed on it, not just -1/-1 counters.

Damage from a source with infect has no effect on Melira's Keepers. No -1/-1 counters are placed on it, and no damage is marked on it. The damage is still dealt for purposes of effects that care about damage, such as lifelink.

If Melira's Keepers would enter with a counter on it, it simply enters without that counter.

If a creature with a counter on it becomes a copy of Melira's Keepers, those counters will remain.