How do I configure Ninject to create a singleton PetaPoco instance

Question

Getting to grips with Ninject and at the moment and I have the Ninject configuration in my MVC application (which I want to figure out how not to do, but that is a different question).

I have several other working configurations, but I don't know how to set it up with PetaPoco.

These are two ways I've tried:

Bind<PetaPoco.Database>().ToConstructor(
    context => new PetaPoco.Database("connectionStringName")
).InSingletonScope();


Bind<PetaPoco.Database>().ToMethod(
    context =>
    {
       var db = new PetaPoco.Database("connectionStringName");
       return db;
    }
).InSingletonScope();

The error I get:

Error activating Database using implicit self-binding of Database

Several constructors have the same priority. Please specify the constructor using ToConstructor syntax or add an Inject attribute.

Constructors:

Database(string connectionStringstring providerName)

Database(string connectionStringDbProviderFactory provider)

How can I set up binding so that a single instance of PetaPoco is passed around?

UPDATE:

I have just seen a fork of PetaPoco called NPoco which contains an IDatabase interface so maybe this would be the better option?

UPDATE 2

I swapped to NPoco and used the IDatabase interface. Ninject picked it up and passed it through no problem. I now need to think about disposing of the database object.