You can make use of Azure and host you database there. Your application can then connect to this database. Of course this means that the client computers must be able to connect to internet to reach this database.
This[
^] page should give you some help to begin. Here is high level information:
1. Create your account and database on MS Azure.
2. Get the connection string from Azure portal.
3. Use this connection string in your application standard ADO.Net code.
4. Allow client IPs in your SQL database firewall. This can be done using Azure web portal.
Unfortunately, if the client computers have dynamic IPs, you will either need to ask them to get static IPs so that could be used or at least get the range within which the client IPs will be present.