Mysqldump from the Amazon RDS
Have you tried mysqldump using --single-transaction ? In this way it doesn't lock the table for threads doing SQL,DML operations provided no DDL statements should be issued and you will get the backups for conistent states only. This will be efficient  only for innodb tables. Below url might give some insights about the option.

http://dev.mysql.com/doc/refman/5.1/en/mysqldump.html#option_mysqldump_single-transaction