How do I invert BooleanToVisibilityConverter?

Write your own is the best solution for now. Here is an example of a Converter that can do both way Normal and Inverted. If you have any problems with this just ask.

[ValueConversion(typeof(bool), typeof(Visibility))]
public class InvertableBooleanToVisibilityConverter : IValueConverter
{
    enum Parameters
    {
        Normal, Inverted
    }

    public object Convert(object value, Type targetType,
                          object parameter, CultureInfo culture)
    {
        var boolValue = (bool)value;
        var direction = (Parameters)Enum.Parse(typeof(Parameters), (string)parameter);

        if(direction == Parameters.Inverted)
            return !boolValue? Visibility.Visible : Visibility.Collapsed;

        return boolValue? Visibility.Visible : Visibility.Collapsed;
    }

    public object ConvertBack(object value, Type targetType,
        object parameter, CultureInfo culture)
    {
        return null;
    }
}

<UserControl.Resources>
  <Converters:InvertableBooleanToVisibilityConverter x:Key="_Converter"/>
</UserControl.Resources>

<Button Visibility="{Binding IsRunning, Converter={StaticResource _Converter}, ConverterParameter=Inverted}">Start</Button>

using System;
using System.Globalization;
using System.Windows;
using System.Windows.Data;

public sealed class BooleanToVisibilityConverter : IValueConverter
{
    public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
    {
        var flag = false;
        if (value is bool)
        {
            flag = (bool)value;
        }
        else if (value is bool?)
        {
            var nullable = (bool?)value;
            flag = nullable.GetValueOrDefault();
        }
        if (parameter != null)
        {
            if (bool.Parse((string)parameter))
            {
                flag = !flag;
            }
        }
        if (flag)
        {
            return Visibility.Visible;
        }
        else
        {
            return Visibility.Collapsed;
        }
    }

    public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture)
    {
        var back = ((value is Visibility) && (((Visibility)value) == Visibility.Visible));
        if (parameter != null)
        {
            if ((bool)parameter)
            {
                back = !back;
            }
        }
        return back;
    }
}

and then pass a true or false as the ConverterParameter

       <Grid.Visibility>
                <Binding Path="IsYesNoButtonSetVisible" Converter="{StaticResource booleanToVisibilityConverter}" ConverterParameter="true"/>
        </Grid.Visibility>

Implement your own implementation of IValueConverter. A sample implementation is at

http://msdn.microsoft.com/en-us/library/system.windows.data.ivalueconverter.aspx

In your Convert method, have it return the values you'd like instead of the defaults.

There's also the WPF Converters project on Codeplex. In their documentation they say you can use their MapConverter to convert from Visibility enumeration to bool

<Label>
    <Label.Visible>
        <Binding Path="IsVisible">
            <Binding.Converter>
                <con:MapConverter>
                    <con:Mapping From="True" To="{x:Static Visibility.Visible}"/>
                    <con:Mapping From="False" To="{x:Static Visibility.Hidden}"/>
                </con:MapConverter>
            </Binding.Converter>
        </Binding>
    </Label.Visible>
</Label>

Rather than writing your own code / reinventing, consider using CalcBinding:

    // Automatic two way convertion of bool expression to Visibility and 
    // back if target property has such type: description
    
    <Button Visibility="{c:Binding !IsChecked}" /> 
    <Button Visibility="{c:Binding IsChecked, FalseToVisibility=Hidden}" />

CalcBinding is also quite useful for numerous other scenarios.

Write your own convert.

public class ReverseBooleanToVisibilityConverter : IValueConverter
{
    public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
   {
       // your converter code here
   }
}