How do I build a DataTemplate in c# code?

Assuming that you've already set up the ItemsSource etc for drpCreditCardNumberWpf...

//create the data template
DataTemplate cardLayout = new DataTemplate();
cardLayout.DataType = typeof(CreditCardPayment);

//set up the stack panel
FrameworkElementFactory spFactory = new FrameworkElementFactory(typeof(StackPanel));
spFactory.Name = "myComboFactory";
spFactory.SetValue(StackPanel.OrientationProperty, Orientation.Horizontal);

//set up the card holder textblock
FrameworkElementFactory cardHolder = new FrameworkElementFactory(typeof(TextBlock));
cardHolder.SetBinding(TextBlock.TextProperty, new Binding("BillToName"));
cardHolder.SetValue(TextBlock.ToolTipProperty, "Card Holder Name");
spFactory.AppendChild(cardHolder);

//set up the card number textblock
FrameworkElementFactory cardNumber = new FrameworkElementFactory(typeof(TextBlock));
cardNumber.SetBinding(TextBlock.TextProperty, new Binding("SafeNumber"));
cardNumber.SetValue(TextBlock.ToolTipProperty, "Credit Card Number");
spFactory.AppendChild(cardNumber);

//set up the notes textblock
FrameworkElementFactory notes = new FrameworkElementFactory(typeof(TextBlock));
notes.SetBinding(TextBlock.TextProperty, new Binding("Notes"));
notes.SetValue(TextBlock.ToolTipProperty, "Notes");
spFactory.AppendChild(notes);

//set the visual tree of the data template
cardLayout.VisualTree = spFactory;

//set the item template to be our shiny new data template
drpCreditCardNumberWpf.ItemTemplate = cardLayout;

You can use the same way I have set the ToolTip on the TextBlocks to set other properties such as margins.

The full version

var ms = new MemoryStream(Encoding.UTF8.GetBytes(@"<DataTemplate xmlns=""http://schemas.microsoft.com/winfx/2006/xaml/presentation""
                                                                 xmlns:x=""http://schemas.microsoft.com/winfx/2006/xaml""                                                                             
                                                                 xmlns:c=""clr-namespace:MyApp.Converters;assembly=MyApp"">
        <DataTemplate.Resources>
            <c:MyConverter x:Key=""MyConverter""/>
        </DataTemplate.Resources>
        <TextBlock Text=""{Binding ., Converter={StaticResource MyConverter}}""/>
      </DataTemplate>"));
var template = (DataTemplate)XamlReader.Load(ms);

var cb = new ComboBox { };
//Set the data template
cb.ItemTemplate = template;