RichTextBox will allow you to use html to specify the color. Another alternative is using a listbox and using the DrawItem event to draw how you would like. AFAIK, textbox itself can't be used in the way you're hoping.
Assuming WinForms, the ForeColor property allows to change all the text in the TextBox
(not just what you're about to add):
TextBox.ForeColor = Color.Red;
To only change the color of certain words, look at RichTextBox.
Source: Stackoverflow.com