Though credit is extremely tight in today's market, it is not impossible to get by any means. Since you've indicated that you have no capital or credit to work with, it's going to be even harder for you so you need to be as realistic as possible.
The first thing I would recommend is that you broaden your outlook from a specific focus on an ice cream business to a much wider search for any good, solid business that might be available. I would look into businesses for sale advertising (newspaper and internet) and contact business brokers as well. What you're looking for is a seller that's willing to carry a contract back for most or all of the purchase price. This isn't easy to find but it is possible, especially if the business is not currently very profitable.
In that case, the chances are that the seller isn't having any more luck selling than you probably are buying. Sometimes it is helpful to offer to work in the business for some period of time for very low wages in order to learn the business and give the seller more confidence that you'll be able to run the business successfully and make your payments to him if he sells to you.
The other best option for you to consider is an angel investor. This is a person that has plenty of money and is willing to back you in the purchase of a business. This might be a relative or someone you've worked for in the past. In any case, though these types of people are hard to find it never hurts to ask and explore your options with anyone you think would be qualified in this area.