You can run a SQL query in your install script:
$installer->run("ALTER TABLE `{$this->getTable('your/table')}` CONVERT TO CHARACTER SET utf8 COLLATE utf8_general_ci;");
Edit:
I think there is no built-in method to change tables charset. There is only a method to change columns ...
$installer->getConnection()->changeColumn($tableName, $oldColumnName, $newColumnName, $definition);
Example from magento update script:
$installer->getConnection()->changeColumn($this->getTable('sales_flat_quote_item'),
'weee_tax_applied', 'weee_tax_applied',
'text CHARACTER SET utf8'
);