int position = 1;
foreach (var i in yourItemList)
{
   youranotherProperty = "";
   ItemBackgroundColor = (position % 2 == 0)? "Green" : "Red" ;
   position++;
}

public class AlternateColorDataTemplateSelector : DataTemplateSelector
{
    public DataTemplate EvenTemplate { get; set; }
    public DataTemplate UnevenTemplate { get; set; }

    protected override DataTemplate OnSelectTemplate(object item, BindableObject container)
    {
        // TODO: Maybe some more error handling here
        return ((List<string>)((ListView)container).ItemsSource).IndexOf(item as string) % 2 == 0 ? EvenTemplate : UnevenTemplate;
    }
}

<ContentPage xmlns="http://xamarin.com/schemas/2014/forms" xmlns:x="http://schemas.microsoft.com/winfx/2009/xaml" xmlns:local="clr-namespace:AlternateRowColorSample" x:Class="AlternateRowColorSample.MainPage">
    <ContentPage.Resources>
        <ResourceDictionary>
            <DataTemplate x:Key="evenTemplate">
                <ViewCell>
                    <Grid BackgroundColor="White">
                        <Label Text="{Binding .}" HorizontalOptions="Center" VerticalOptions="Center" />
                    </Grid>
                </ViewCell>
            </DataTemplate>
            <DataTemplate x:Key="unevenTemplate">
                <ViewCell>
                    <Grid BackgroundColor="LightGray">
                        <Label Text="{Binding .}" TextColor="White" HorizontalOptions="Center" VerticalOptions="Center" />
                    </Grid>
                </ViewCell>
            </DataTemplate>
            <local:AlternateColorDataTemplateSelector x:Key="alternateColorDataTemplateSelector"
                EvenTemplate="{StaticResource evenTemplate}"
                UnevenTemplate="{StaticResource unevenTemplate}" />
        </ResourceDictionary>
    </ContentPage.Resources>

    <ListView ItemTemplate="{StaticResource alternateColorDataTemplateSelector}" ItemsSource="{Binding Items}">

    </ListView>
</ContentPage>