You *possibly* may be able to qualify, but you should know that it appears the USCIS is going to be very strict with criminal history. Thus, it is also very possible that if you apply, you may be denied.
I would strongly encourage you not to proceed without at least consulting with (and ideally hiring) an experienced immigration attorney who can advocate for you as to why your situation should not make you ineligible. Keep in mind that there is not an appeal process if you apply and are denied. Thus, you likely will want an experienced immigration attorney who can evaluate your eligibility and advise you on obtaining the proper documentation, help you adequately answer any potential request for additional evidence or information if you receive one, and submit a strong eligibility brief or legal memorandum on your behalf if you do decide to file for deferred action in spite of the potential risks.
If you need assistance finding immigration attorneys, you can look here on Avvo, at www.aila.org or www.immigrationlawhelp.org. Do not be afraid to ask any attorney you consider about his/her experience with immigration litigation and criminal immigration. Unfortunately, I see some very poorly written legal memos and briefs, even from some attorneys, so it is important to work with someone who is reputable and has a proven track record in these kinds of cases.
Ms. Doerrie's answer to your question is general in nature, as not all facts and circumstances relating to the specific person(s) and situations involved are known to her. Ms. Doerrie recommends consulting with an immigration attorney regarding your specific facts and circumstances prior to making any legal decision or submitting any form or application. This response does not constitute legal advice or create an attorney/client relationship.
I agree with Ms. Doerrie.
Franco Capriotti - Senior Legal Counsel - Capriotti International Law – 503-803-0055
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IMMIGRATION LAW PROFESSOR for 10 years -- LEGAL DISCLAIMER: This answer is offered for informational purposes only. It does not constitute an attorney-client relationship.