You need to specify the trigger as part of a style -- the Triggers collection on the Button itself can only contain event triggers. With that in mind, a DataTrigger works fine. However, there is a wrinkle: the value from the Trigger Setter won't overwrite a local Content property. So you have to set the default Content in the Style as well. Here's how it looks:
<Button> <!-- Note no content set directly on button -->
<Button.Style>
<Style TargetType="Button">
<Setter Property="Content" Value="You may write!!!" /> <!-- Here is the 'normal' content -->
<Style.Triggers>
<!-- Here is how we bind to another control's property -->
<DataTrigger Binding="{Binding IsReadOnly, ElementName=textBox}" Value="True">
<Setter Property="Content" Value="NO NO NO" /> <!-- Here is the 'override' content -->
</DataTrigger>
</Style.Triggers>
</Style>
</Button.Style>
</Button>