Well the first point is don't ask for payment after the work is done. No one will pay because you've already solved their pain. You're in a weaker position at that point.
Tell them how much you charge before you start work and ask if they want you to start work. It can only go one of two ways.
The easiest way to convince them is to compare it to sales. If they are an electrician with an average job of $500, that website only needs to earn them two extra jobs per year to break even.
But the easiest way is to be a sociopath and not care. Ask the question and they will either say yes or no. No one is going to assassinate you for pitching a marketing website to them.
If they say yes, do you care where the money has come from? Would it matter if that was their last $1k? If they're loaded would you feel more confident? What if you do a great job and then it turns out that money came from illegal sources?
What about if they say no? Will you stay awake at night worrying that their business is losing work because people think they're weird for not having a website? What if your marketing website lands them a big client because of the "authenticity factor" of having a professional marketing website?
None of these things actually matter. But getting paid $1k feels good, especially if you've done a good job and earned it. :)