Here's a sample that might help you out.  This custom style should draw a red circle inside the bar for the data point.

<UserControl x:Class="SL_xamWebChart.MainPage"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    xmlns:igChart="clr-namespace:Infragistics.Silverlight.Chart;assembly=InfragisticsSL4.Controls.Charts.XamWebChart.v10.3"
    mc:Ignorable="d"
    d:DesignHeight="300" d:DesignWidth="400">
    <UserControl.Resources>
        <Style x:Key="DataPointStyle1" TargetType="igChart:BoxChartDataPointTemplate">
            <Setter Property="Template">
                <Setter.Value>
                    <ControlTemplate TargetType="igChart:BoxChartDataPointTemplate">
                        <Canvas x:Name="RootElement">
                            <Line x:Name="LineMin" Stroke="{TemplateBinding Stroke}" StrokeThickness="{TemplateBinding StrokeThickness}"/>
                            <Line x:Name="LineMax" Stroke="{TemplateBinding Stroke}" StrokeThickness="{TemplateBinding StrokeThickness}"/>
                            <Line x:Name="LineSpan" Stroke="{TemplateBinding Stroke}" StrokeThickness="{TemplateBinding StrokeThickness}"/>
                            <Line x:Name="LineMedian" Stroke="{TemplateBinding Stroke}" StrokeThickness="{TemplateBinding StrokeThickness}"/>
                            <Border x:Name="BoxDataPoint" BorderBrush="{TemplateBinding Stroke}" Background="{TemplateBinding Fill}" BorderThickness="{TemplateBinding BorderThickness}">
                                <Ellipse Stretch="Uniform" Fill="red"/>
                            </Border>
                        </Canvas>
                    </ControlTemplate>
                </Setter.Value>
            </Setter>
        </Style>
    </UserControl.Resources>

    <Grid x:Name="LayoutRoot" Background="White">
        <igChart:XamWebChart Name="chart1" Height="200" Width="300" VerticalAlignment="Top">
            <igChart:XamWebChart.Series>
                <igChart:Series ChartType="Box" Label="Box XYZ">
                    <igChart:Series.DataPoints>
                        <igChart:DataPoint Label="10/10/2007">
                            <igChart:DataPoint.ChartParameters>
                                <igChart:ChartParameter Type="Max" Value="50" />
                                <igChart:ChartParameter Type="Min" Value="5" />
                                <igChart:ChartParameter Type="Q1" Value="9" />
                                <igChart:ChartParameter Type="Q2" Value="25" />
                                <igChart:ChartParameter Type="Q3" Value="40" />
                            </igChart:DataPoint.ChartParameters>
                        </igChart:DataPoint>
                        <igChart:DataPoint Label="10/11/2007" Style="{StaticResource DataPointStyle1}" Fill="Green">
                            <igChart:DataPoint.ChartParameters>
                                <igChart:ChartParameter Type="Max" Value="60" />
                                <igChart:ChartParameter Type="Min" Value="10" />
                                <igChart:ChartParameter Type="Q1" Value="15" />
                                <igChart:ChartParameter Type="Q2" Value="25" />
                                <igChart:ChartParameter Type="Q3" Value="45" />
                            </igChart:DataPoint.ChartParameters>
                        </igChart:DataPoint>
                    </igChart:Series.DataPoints>
                </igChart:Series>
            </igChart:XamWebChart.Series>
        </igChart:XamWebChart>
    </Grid>
</UserControl>