Add a DbProviderFactory without an App.Config

Update for EF 6.0+

You can add a DbProviderFactory by registering a IDbDependencyResolver and resolving for the type DbProviderFactory. An example of this is below:

static class Program
{
    [STAThread]
    static void Main()
    {
        System.Data.Entity.DbConfiguration.Loaded += (_, a) => {
            a.AddDependencyResolver(new MyDependencyResolver(), true);
        };  

        Application.Run(new Form1());
    }
}

class MyDependencyResolver : System.Data.Entity.Infrastructure.DependencyResolution.IDbDependencyResolver {

    public object GetService(Type type, object key) {

        // Output the service attempting to be resolved along with it's key 
        System.Diagnostics.Debug.WriteLine(string.Format("MyDependencyResolver.GetService({0}, {1})", type.Name, key == null ? "" : key.ToString()));

        if (type == typeof(System.Data.Common.DbProviderFactory)) {

            // Return whatever DbProviderFactory is relevant
            return new MyDbProviderFactory(); 

        }else if(type == typeof(System.Data.Entity.Infrastructure.IProviderInvariantName) && key != null && key == "MyDbProviderFactory"){

            // Return the Provider's invariant name for the MyDbProviderFactory
            return new MyProviderInvariantName();

        }

        return null;
    }

    public IEnumerable<object> GetServices(Type type, object key) {
        return new object[] { GetService(type, key) }.ToList().Where(o => o != null);
    }
}

you may have to resolve for some additional types as well depending upon what type of overriding you're needing to do and how your project is setup. Basically just start with the code above and continue to debug until you've determined all the services you need to resolve for given your specific requirements.

You can read more about EF dependency resolution at the links below:

• http://msdn.microsoft.com/en-us/data/jj680697.aspx
• https://entityframework.codeplex.com/wikipage?title=EF%20Configuration%20and%20Extensibility
• https://entityframework.codeplex.com/wikipage?title=Rebuilding%20EF%20providers%20for%20EF6

Additionally, you can do this configuration by overriding DbConfiguration as described in the first link above.

LATE ANSWER:

You can always directly get a factory like this:

DbProviderFactory factory = System.Data.SQLite.SQLiteFactory.Instance;
// (note that the rest of the code is still provider-agnostic.)

Or use your IoC container to resolve the DbProviderFactory, e.g.:

container.RegisterInstance<DbProviderFactory>(SQLiteFactory.Instance);

I prefer not to use the DbProviderFactories.GetFactory because of its limitation of requiring a configuration file (or a hack like in @JoshRiver's answer).

All DbProviderFactories.GetFactory does is, it looks up the registered assembly-qualified name of the factory type using the provider name, and then it gets the value of the static Instance property using reflection.

If you don't want to use the configuration, one of the methods above might be more convenient depending on your use case.

JoshRivers above posted a solution for SQLite. This can in fact be used for other adapters as well- I was able to get it working for MySQL using his example. I have wrapped this into something a bit more generic. This should be run once the application starts and is for the .NET connector version 6.6.5.0 (but I imagine it is good for other versions as well.)

string dataProvider = @"MySql.Data.MySqlClient";
string dataProviderDescription = @".Net Framework Data Provider for MySQL";
string dataProviderName = @"MySQL Data Provider";
string dataProviderType = @"MySql.Data.MySqlClient.MySqlClientFactory, MySql.Data, Version=6.6.5.0, Culture=neutral, PublicKeyToken=c5687fc88969c44d";

bool addProvider = true;
var dataSet = ConfigurationManager.GetSection("system.data") as DataSet;
foreach (DataRow row in dataSet.Tables[0].Rows)
{
    if ((row["InvariantName"] as string) == dataProvider)
    {
        // it is already in the config, no need to add.
        addProvider = false;
        break;
    }
}

if (addProvider)
    dataSet.Tables[0].Rows.Add(dataProviderName, dataProviderDescription, dataProvider, dataProviderType);

The following will probably cause sunspots and overthrow western civilization. It may even cause a debate about Duct Tape Programming (make it stop!), but it works (for now)

try
{
    var dataSet = ConfigurationManager.GetSection("system.data") as System.Data.DataSet;
    dataSet.Tables[0].Rows.Add("SQLite Data Provider"
    , ".Net Framework Data Provider for SQLite"
    , "System.Data.SQLite"
    , "System.Data.SQLite.SQLiteFactory, System.Data.SQLite");
}
catch (System.Data.ConstraintException) { }