# The date and target (1 is Monday, 7 Sunday)
my $dt = DateTime->new(year => 1998, month => 4, day => 3); # Friday
my $target = 6; # Saturday

# Get the day of the week for the given date
my $dow = $dt->day_of_week();

# Apply the corrections
my ($prev, $next) = ($dt->clone(), $dt->clone());

if ($dow == $target) {
    $prev->add( days => -7 );
    $next->add( days =>  7 );
} else {
    my $correction = ( $target - $dow + 7 ) % 7;
    $prev->add( days => $correction - 7 );
    $next->add( days => $correction );
}

# $prev is 1998-03-28, $next is 1998-04-04