Did you inquire about getting a small HELOC for the flooring replacement, or just for the land purchase?
Perhaps a request for $10-$15K would be more palatable to the bank than $50K, especially if you merely stated that the funds would be used for a home improvement, without specifying which home…
I’ve not worked with a private money lender before, but have seen good reviews about Connected Investors Exchange (link in my previous post).
My understanding is that CIX utilizes a kind of crowd sourcing for loans: it has vetted a large pool of investors who want to finance new construction, purchases, and rehabs; I would imagine that there is likely someone in that pool who would be willing to fund a smaller project, such as repairs, rehabs, or vacant land purchases.
My further understanding is that the investors loan on the asset (real estate), rather than on the borrower (income, credit history, etc.); should the borrower default, the lender simply forecloses on the property.
Another source for a small loan would be local investors. Unless you are in a rural area, there is likely some form of Real Estate Investors organization nearby that you can ask about sources of funding for small projects (less than $150K).
MeetUp is one source to check to see if there are any such organizations in your area. Scroll to the bottom of its homepage and click on Career & Business (bottom right corner); any REI organizations hosting upcoming events should pop up.
If you sign up for a free membership, there is a way to search through all of the interest groups in your desired area (music, dance, language, cooking, wine, outdoors, pets, etc.) and perhaps find a way to contact the real estate group host directly, even if there are no upcoming events scheduled.