Thanks, Rob. One working solution is to use ->allocate(). Another is to use Gtk2::Gdk::Cairo::Context instead of Gnome2::Canvas.

Both are posted below, in case anyone is interested.

#!/usr/bin/perl
use strict;
use diagnostics;
use warnings;

use Gtk2 '-init';
use Glib qw(TRUE FALSE);
use Gnome2::Canvas;

# Draw a Gtk2 window
my $window = Gtk2::Window->new();
$window->signal_connect('delete_event' => sub { Gtk2->main_quit; });
$window->set_default_size(500, 500);
$window->set_border_width(5);

my $vBox = Gtk2::VBox->new(FALSE, 0);
$window->add($vBox);

# Draw a Gtk2::Frame containing a Gnome2::Canvas
# The frame should be as long as possible, but only 50 pixels high 
my $frame = Gtk2::Frame->new(undef);
$frame->set_border_width(0); 
$frame->set_size_request(-1, 50); 

my $canvas = Gnome2::Canvas->new();
$frame->add($canvas);
$vBox->pack_start($frame, FALSE, FALSE, 0);

# The ->show_all() call here makes everything work (for some reason)
$window->show_all();

my $rect = $canvas->allocation();
$canvas->set_scroll_region(
        0,
        0,
        $rect->width,
        $rect->height,
);

# Draw a red bar, almost as long as the frame, but with a fixed
#   height, centred in the middle
my ($width, $height) = $canvas->get_size();
# (The Gtk2::Frame is 490x50, so the Gnome2::Canvas should be 488x48)
#print "canvas w $width h $height\n";

my $canvasItem = Gnome2::Canvas::Item->new(
    $canvas->root(),
    'Gnome2::Canvas::Rect',       
     x1 => 20,                                    
     y1 => 20,                                                  
     x2 => ($width - 20),
     y2 => ($height - 20),          
     fill_color => '#FF0000',
     outline_color => '#000000',
);

$canvasItem->raise_to_top();
  
$window->show_all();
Gtk2->main;
[download]

Second one...

#!/usr/bin/perl
use strict;
use diagnostics;
use warnings;
use Gtk2 '-init';
use Glib qw(TRUE FALSE);
# Draw a Gtk2 window
my $window = Gtk2::Window->new();
$window->signal_connect('delete_event' => sub { Gtk2->main_quit; });
$window->set_default_size(500, 500);
$window->set_border_width(5);

my $eBox = Gtk2::EventBox->new();
$eBox->set_app_paintable(TRUE);
$eBox->signal_connect('expose_event' => \&draw_event_box);

my $Label1 = Gtk2::Label->new("Label1");
$Label1->set_markup("<span foreground='green' font='25'>Label1</span>"
+);

my $Label2 = Gtk2::Label->new("Label2");
$Label2->set_markup("<span foreground='red' font='25'>Label2</span>");

my $vBox = Gtk2::VBox->new(FALSE, 0);
$vBox->pack_start_defaults($Label1);
$vBox->pack_start_defaults($Label2);

$eBox->add($vBox);
$window->add($eBox);

$window->show_all();
Gtk2->main;

sub draw_event_box
{
  my ($widget, $event, $user_data) = @_;
  my $cr = Gtk2::Gdk::Cairo::Context->create( $widget->window );
  my $rectangle = $widget->allocation;

  #Paint background.
  $cr->set_source_rgb(0, 1, 1);
  $cr->paint;

  #Draw yellow line in middle.
  $cr->set_source_rgb(1, 1, 0);
  $cr->set_line_width(10);
  $cr->move_to(0, ($rectangle->height) / 2);
  $cr->line_to($rectangle->width, ($rectangle->height) / 2);
  $cr->stroke();

  #Draw frame.
  $cr->set_source_rgb(0, 0, 1);
  $cr->set_line_width(15);
  $cr->rectangle(0, 0, $rectangle->width, $rectangle->height);
  $cr->stroke();
       
  return FALSE;
}
[download]