To answer your question, offering a guarantee that minimizes their risk should do the trick... (i.e. if you dont double the money you pay me in 12 months, Ill give you a refund... assuming you don't damage their site, just the time passing and age alone should produce double what you charge them, even without doing any real SEO..)

However...

I don't see any reason why you would need a full year to show results... There are usually low hanging fruits you can uncover and fix for the first crawl google does showing results within weeks.
If you are promoting content to earn links, than I think 4-6 months is reasonable...

Your best bet is to talk about accumulative efforts, and how the value you provide will build on itself, and it would be a shame if you didn't have a chance to see it through. (i.e. building relationships from outreach to earn links will create new linking opportunities in the future...etc...)

All in all, I do SEO month to month, and i have clients that stuck with me for 5+ years... I guess it really depends what you are actually doing for them...