Variations include seller financing (you'd receive the deed and the owner would finance), contract for deed (the seller would hold the deed until you'd met certain agreed-upon requirements), lease-option (in which you'd lease the property, having the option to purchase it in the future), lease-purchase (in which you'd lease the property, while also having a legally binding purchase agreement), and a number of other ways.
A seller will be most concerned with your ability to meet your future commitments. Thus, for many sellers, it's better if, as you suggest, that your low credit score and other financial difficulties were due to a specific event and not representative of your general attitude toward obligations.
Having enough cash to put 10% down (with seller financing) or the equivalent of 10% down if you pursue some of the other routes (lease-purchase, lease-option) is very good.
What you (and your agent, if you find one to work with...not all will, but the smart ones will) need to be looking for are people who want to sell their houses but are willing to provide financing and hold onto some of their equity for a number of years. In the MLS, you can look for sellers who say they're willing to do lease-options. Also have your agent look through the MLS for properties that are listed both "for sale" and "for rent." They're also prime candidates. Then have your agent look for properties that are currently for rent, but had been for sale. Those are properties that didn't sell, and the owners are now willing to rent them.
If that doesn't turn up enough, do (or have your agent do) a mailing to absentee owners whose houses match your criteria. The mailing should be straightforward--that you'd be interested in purchasing their homes, full-price, but would like the opportunity to lease the property first.
Another possibility is to consider buying a home subject to (so-called "Sub 2") the existing mortgage. In this case, you'd have to find someone who essentially is willing to give you the house. They would give you the deed, and you'd agree to make their mortgage payments until, at some date in the future, you'd refinance it in your own name. The prime prospect for this is someone who is falling behind on their mortgage payments, and just wants out. Your Realtor probably is aware of some of those situations. If not, an ad on CraigsList will produce some willing possibilities.
There are plenty of other ways, too. But one of those, above, will work. Basically, all you need to do is find someone who wants to get rid of their property. And nowadays, that's not difficult to find.