First, I don't know what your application does, but based on the small yearly price, I assume it isn't super-complicated. BUT regardless of how simple your application is, you should negotiate a deal that will bring you thousands or tens of thousands over a period of time. They have likely spend some time finding out about possible solution. Thus, they can easily pay a few thousand dollars immediately if it solves their need and more over a period of time.
However, don't just negotiate on a single price, but strike a deal where support work will bring you recurring revenue on monthly basis.
Try to have several dimensions on which you negotiate, not just the price. You already had a great idea for a negotiation dimension: do you offer it as a white or gray label solution. If they are willing to pay too little, require that your product brand is clearly visible for end users, thus bringing more customers for you in the future. You can negotiate on many things besides the price: the scope of your support, your availability, the response time to support queries, your scalability promise to them, future improvements to product, etc.
By the way, you should probably raise the yearly price of your product for new customers, small or large, anyway. I find it hard to imagine a product that is both so valuable to businesses that they start to use it but so invaluable that a small business owner wouldn't be willing to pay more than 20$/year for it. If they spend a few hours to install and familiarizing themselves with your product, they have already spend more than 20$/year of their own time for it.
However, don't just negotiate on a single price, but strike a deal where support work will bring you recurring revenue on monthly basis.
Try to have several dimensions on which you negotiate, not just the price. You already had a great idea for a negotiation dimension: do you offer it as a white or gray label solution. If they are willing to pay too little, require that your product brand is clearly visible for end users, thus bringing more customers for you in the future. You can negotiate on many things besides the price: the scope of your support, your availability, the response time to support queries, your scalability promise to them, future improvements to product, etc.
Good luck!