Can Espeon's "Solar Suggestion" attack place damage counters onto a Jolteon that can't be hit by effects due to a successful coin flip during its "Agility" attack, or onto a Toxicroak [G] with its "Anticipation" Poke-BODY enabled? If I can't place them, what do I do with the damage counters I removed from my Pokemon?
You cannot place damage counters onto that Jolteon or Toxicroak [G], but you can still remove damage counters from your own Pokemon. If you select a Pokemon under the status of not receiving effects, the damage counters that would be placed onto that Pokemon simply disappear from play.
Source: Undaunted FAQ (2010-09-09), PUI Rules Team (2010-09-09)

Relevant cards

Note: All applicable cards may not be listed below.
COL1_4
HGSS3_2