There's Dumpy the frog.
A simple utility written in PHP that will mirror a directory to an S3 bucket.
Supports cleaning up old backups by means of a keep parameter, which you can use to specify how many copies of the directory backup you want to keep. Older copies will be deleted.
Configuration details are stored in a .env file.
$ git clone git@github.com:jaredh159/dumpy-backups.git
$ cd dumpy-backups
$ composer install
$ cp .env.example .env
$ vim .env
Invoke via SSH or (more likely) cron, like so:
$ php path/to/dumpy backup:create --path=/dir/to/backup --prefix=files/weekly --keep=3