对于您首次描述的场景,正确制定了.When(…)应该有效.

作为.When(…)绑定的替代方法,您还可以使用.Named(“FooBar”)绑定.
然后,计划任务的构造函数需要如下所示：

ctor(Named["FooBar"] DbContext dbContext);

但请注意,这只是(容易)工作,以防您需要将DbContext注入单个构造函数.如果任务具有依赖性,并且这些依赖性也需要相同的DbContext实例,那么它会有点过时.

由于您更新了答案并说是这种情况,我建议采用完全不同的方法：使用请求参数作为When(…)条件与InCallScope绑定相结合的基础.请参阅下面的示例.

支持自己,这是代码:)实现需要ninject.extensions.NamedScope扩展(nuget).
我还使用xUnit和FluentAssertions nuget包来执行测试.

public class Test
{
    // the two implementations are just for demonstration and easy verification purposes. You will only use one DbContext type.
    public interface IFakeDbContext { }
    public class RequestScopeDbContext : IFakeDbContext { }
    public class CallScopeDbContext : IFakeDbContext { }

    public class SoMetask
    {
        public IFakeDbContext FakeDbContext { get; set; }
        public Dependency1 Dependency1 { get; set; }
        public Dependency2 Dependency2 { get; set; }

        public SoMetask(IFakeDbContext fakeDbContext,Dependency1 dependency1,Dependency2 dependency2)
        {
            FakeDbContext = fakeDbContext;
            Dependency1 = dependency1;
            Dependency2 = dependency2;
        }
    }

    public class Dependency1
    {
        public IFakeDbContext FakeDbContext { get; set; }

        public Dependency1(IFakeDbContext fakeDbContext)
        {
            FakeDbContext = fakeDbContext;
        }
    }

    public class Dependency2
    {
        public IFakeDbContext FakeDbContext { get; set; }

        public Dependency2(IFakeDbContext fakeDbContext)
        {
            FakeDbContext = fakeDbContext;
        }
    }

    public class TaskScheduler
    {
        private readonly IResolutionRoot _resolutionRoot;

        public TaskScheduler(IResolutionRoot resolutionRoot)
        {
            _resolutionRoot = resolutionRoot;
        }

        public SoMetask CreateScheduledTaskNow()
        {
            return _resolutionRoot.Get<SoMetask>(new NonRequestScopedParameter());
        }
    }

    public class NonRequestScopedParameter : Ninject.Parameters.IParameter
    {
        public bool Equals(IParameter other)
        {
            if (other == null)
            {
                return false;
            }

            return other is NonRequestScopedParameter;
        }

        public object GetValue(IContext context,ITarget target)
        {
            throw new NotSupportedException("this parameter does not provide a value");
        }

        public string Name
        {
            get { return typeof(NonRequestScopedParameter).Name; }
        }

        // this is very important
        public bool ShouldInherit
        {
            get { return true; }
        }
    }

    [Fact]
    public void FactMethodName()
    {
        var kernel = new StandardKernel();

        // this is the default binding
        kernel.Bind<IFakeDbContext>().To<RequestScopeDbContext>();

        // this binding is _only_ used when the request contains a NonRequestScopedParameter
        // in call scope means,that all objects built in the a single request get the same instance
        kernel.Bind<IFakeDbContext>().To<CallScopeDbContext>()
            .When(x => x.Parameters.OfType<NonRequestScopedParameter>().Any())
            .InCallScope();

        // let's try it out!
        var task = kernel.Get<SoMetask>(new NonRequestScopedParameter());

        // verify that the correct binding was used
        task.FakeDbContext.Should().BeOfType<CallScopeDbContext>();

        // verify that all children of the task get injected the same task instance
        task.FakeDbContext.Should()
            .Be(task.Dependency1.FakeDbContext)
            .And.Be(task.Dependency2.FakeDbContext);
    } 
}

正如您所说,由于任务调度程序不使用IoC来创建任务,因此它只支持无参数构造函数.在这种情况下,您可以使用DependencyResolver.Current(但请注意,我不是asp.net / MVC的专家,所以我没有声称这是线程安全或100％可靠地工作)：

public class TaskExecutor : ITask
{
    public TaskExecutor()
        : this(DependencyResolver.Current.GetService<IResolutionRoot>())
    {}

    internal TaskExecutor(IResolutionRoot resolutionRoot)
    {
        this.resolutionRoot = resolutionRoot;
    }

    public void Execute()
    {
        IFooTask actualTask = this.resolution.Get<IFooTask>(new NonRequestScopedParameter());
        actualTask.Execute();
    }
}