Green parties started to form in the 1980s, and there have been few invasions of democratic nations since then. Without wanting to do into who counts as democratic, if we accept Green parties as being relevant only in western European politics so far, then the 1982 invasion of the Falklands becomes the only incident to consider.
List of Invasions on Wikipedia
This predates the founding of the Green Party in the UK, but its precessor the Ecology Party existed. I was not able to find their position on the Falklands war, but anyway I would consider them rather fringe compared to the extant Green parties.
I am aware of mainstream Green Parties in Germany, Austria and Finland. Of these, I am positive that those in Germany and Austria consider an invasion of their countries as far too implausible to have a policy on it. Having a border to Russia, there may be more concern in Finland, but not being able to read Finnish, I can't follow the details here. The Finnish Green party is in favour of abolishing the draft.
If you want to see how a Green party has handled a clash between pacifism and other values, I agree with o.m. that the debate surrounding the German Green parties support for the German involvement in the Kosovo conflict is going to be your best bet. This was not merely remarkable because a Green party support military action in government, but because the Federal Republic of Germany had adhered to a "no armed German soldiers on foreign ground" policy until then. Germany's prior involvement in eg UK peacekeeping operations were restricted to unarmed roles.