The point we made in class was that piece of paper is just part of the realtors paperwork checklist.  So, get them a piece of paper. Here are a suggestions on where to get those pieces of paper:

1. A hard money lender.  Find out who the hard money lenders are in your area.  Find out which one or ones will provide you with a pre-approval letter. 
2. Do you know a private lender who could write a letter like that for you?  Just because you get a letter from a private lender, it doesn’t mean that it needs to be the source of those funds.  You don’t need to get a different letter for each property in which you submit an offer. 
3. You could also give the lender a bank statement for a line of credit.  If you don’t have a home equity line of credit, you might consider getting one.  This is just as good as cash in the eyes of a lender looking to sell a property.

The point is, just make it easy for your realtor.  Make it easy for the seller to see that you have the money to close.  Then, just keep firing out offers until you get one.