You could possibly take out a $40,000 home equity loan on your residence, a second mortgage on another investment property, a cash advance on a credit line, a 401-K loan, a personal loan from a bank, credit union, friend, relative, or business associate.
If you can't do any of these, stop here and work on your personal finances until your net worth allows you to borrow $40,000 unsecured.
It seems like with $100K down and only a $40K loan you shouldn't have any trouble finding a lender, so long as you are putting the loan against the property you're buying. However, I doubt you'll be able to find a bridge loan these days - but you could try. Any kind of equity loans are tough right now, and if your other properties are for sale, you won't be able to do a conventional Home Equity Line.
Perhaps you can get a loan against an retirement account? You can also try a signature loan or advance from a credit card - but you better be sure you're comfortable with the terms. Look not just at the real estate liens you can get, but also other assets you have