First, decide where you would want to go. In the knowledge that I have learned previously (I worded it like this because it’s subject to change), Ireland is a pretty easy place to immigrate to. Not Northern Ireland, but The Republic of Ireland. North Ireland is part of the UK and while the requirements to go there can be met, Ireland is easier than that, but I digress…
Once you figured out where you want to go, start looking for jobs in country. Depending on what type of GS employee or contractor you are, there’s a good chance that there is a demand for it in different countries. Essentially, just job hunt.
Now, a personal suggestion I would like to make is if and when you interview, do not mention that your trying to leave the country due to political strife. Say something along the lines of “I wish to experience a life outside of the United States, and would like for my child to be versed in different world views, opinions, and cultures”.
And why do you think that?