Вы можете использовать:
void AppendText(RichTextBox box, Color color, string text)
{
int start = box.TextLength;
box.AppendText(text);
int end = box.TextLength;
// Textbox may transform chars, so (end-start) != text.Length
box.Select(start, end - start + 1);
box.SelectionColor = color;
// could set box.SelectionBackColor, box.SelectionFont, etc...
box.SelectionLength = 0; // clear
}
, а затем
AppendText(rtb, Color.Red, "line1");
AppendText(rtb, Color.Blue, "line2");