Well, honestly, the first thing you should do is raise your fees so that you can afford some advertising.
In the situation that you describe, ie. your "target" population, the best thing that you can do is to create a website that is designed specifically toward Expatriates. There are many organizations that provide the expertise to develop websites from their pro-forma guides that may easily be "personalized" toward the audience that you are targeting. This will afford you a quick way to get a professionally designed website at a minimal cost. Check out a number of these organizations by searching for "Tax Preparer Organizations" or "Tax Preparer Trade Organizations", etc. Once you have that established, put your money into one of the various services that will place you high in the search results for terms that Expatriates are likely to use to find a Tax Preparer. Combine that information with your own ideas & you should be off & running. There are other avenues to build this business, and those may take longer to develop; one that comes to mind quickly is to sell your service to the various companies that have employees serving overseas. Many of these organizations provide a tax preparation service to their employees as an employee benefit. When I worked at one of the then "Big Eight" CPA firms, many of our international clients provided this type of service (as well as other financial planning services) to their employees by engaging us to send a representative overseas to where these employees were located to meet with their employees and obtain the information necessary to prepare their tax returns on an annual basis. Although you probably would not be able to secure one of these major customers, it's a service you could easily provide remotely, communicating over the internet, perhaps to smaller companies who only have a few employees located overseas. Again, in this current era, a website would be essential to develop the business you are targeting.
Hope this helps to stimulate your thinking & gives you something to investigate to see if you can find a direction to follow to get started on your objective of serving Expatriates. Good Luck, I think you've got a great idea.
PS If you want to speak with me directly, we have an option of providing an additional service of a telephone consultation, where we can speak with each other in real time.