Girlfriend lives in Ireland but no Visa.

I am an Irish citizen and my girlfriend who is a U.S citizen lives with me in Donegal,Ireland. The thing is that she came here without a visa. She has been living with me for the past 6 months this year and I know it's past the 90 days policy. She applied for a pps number and got it. I don't know why the Social Welfare place gave it to her because they kept on telling that she would need a visa for living here, getting a job or going to school. Now me and her are just worried that she will get deported back to the U.S. She is a really hard worker. But the thing is that she can't find a stable job. All work she can grab right now are child minding jobs.Is there anyway that I can petition her to live here or what can I do. Please we really need help to sort this matter.

None really - except marrying her, moving to NI (or other EU State) and applying for EEA permit.

I overstayed on my student visa to stay with my bf, we got married in Copenhagen and return back to Ireland without any problem at the airport, I got 90days permission to re-register but when we went together for the appointment at the Garda National Immigration Bureau Registration office, they refused to proceed my application due to their suspicious of my overstaying (+They have my GINB card recorded)

I need to apply my permission to stay using route B- http://www.inis.gov.ie/en/INIS/Pages/WP07000024

This is just for your information.

We will give up on the application as we know that the process will be really long (6-9months) and we probably need a lawyer to help us.