As of 2024-11-06, the accepted answer is outdated.
According to the same documentation linked in that answer (https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/USER_WorkingWithParamGroups.Copying.html), the updated command is:
aws rds copy-db-parameter-group \
--source-db-parameter-group-identifier "${SOURCE_ID}" \
--target-db-parameter-group-identifier "${TARGET_ID}" \
--target-db-parameter-group-description "${TARGET_DESCRIPTION}"