OK, what does the form give as the reason for deporation? Probably that she was present without a legal status or that she was working witout permission?
In that case, you might have success with a waiver application. It will probably take several years to get a waiver approved, however.
Immigrati&on Lawyer
Over eight years of experience practicing immigration law.
OK, so she was excluded from the country at the port of entry by a Customs and Border Protection officer. How long ago was this? The reason may have been that they found that she had immigrant intent. In other words, she showed up with a visitor's visa and they found out that she had a boyfriend in the US so they denied her entry for fear that she would get married and apply for permanent residence. I know that seems like a strange way of thinking and that it assumes more than the government should be able to assume, but it happens everyday.
I would do a freedom of information act request at the port of entry where she was denied admission. This will give you the exact reason for the exclusion. It will take a long time, so in the interim you can get married and start the green card process in the US. Then, when she goes to the Consulate, she can apply for a waiver if there is one available. By then, you should have the results of the request and know whether a waiver is available. If the waiver is granted, then she can enter the US as either a permanent resident or a K-3. If you utilize the K-3 route, then you will need to apply for permanent residence once she is admitted.
If you do not want to get married right away, you can utilize the K-1 fiance route. Once she enters, she will have 90 days to marry and then needs to apply for lawful permanent residence.