I tried show_text() with a unicode string and it worked OK.
Could you attach a minimal example which calls show_text() and raises an
exception, and calls PyGTK/gtk.Button and works OK, so I can see the problem.

Sure.  (FYI, this is with Cairo and PyCairo 1.0.2 in Debian unstable.)

Here's my sample program:

import cairo
surface = cairo.ImageSurface(cairo.FORMAT_ARGB32, 400, 400)
c = cairo.Context(surface)
c.set_source_rgb(1.0, 0.0, 0.0)
c.select_font_face("FreeSerif", cairo.FONT_SLANT_NORMAL, cairo.FONT_WEIGHT_NORM\AL)
c.set_font_size(72)
c.move_to(100, 200)
c.show_text("hello") # ***
c.stroke()
surface.write_to_png("cairotext.png")

The line marked *** is the interesting one:

- as written above, with "hello" (a str, all ASCII chars) it works fine

- with u"\u0633" (a unicode string with non-ASCII chars), it gives this error:
Traceback (most recent call last):
  File "cairotext.py", line 11, in ?
    c.show_text(u"\u0633")
UnicodeEncodeError: 'ascii' codec can't encode character u'\u0633' in position
0: ordinal not in range(128)

- with u"\u0633".encode("UTF-8") it works fine


In PyGTK, this works fine:

import gtk
w = gtk.Window()
b = gtk.Button(u"hello, world!  \u0633")
w.add(b)
w.show_all()
gtk.main()

Fixed show_text() to accept string or unicode objects.
Also did the same for some other cairo functions that accept UTF-8 format strings.

	* cairo/pycairo-context.c (__PyBaseString_AsUTF8): new function.
	(pycairo_select_font_face, pycairo_show_text, pycairo_text_extents)
	(pycairo_text_path):
	allow the string argument to be a unicode or string object, and convert
	to UTF-8 encoding.