THE ANSWER IS CURLY BRACKETS!
This is how I did it; it's not the prettiest way to skin a cat...
#!/bin/bash input=$1 output=$2 cp $input ${output}_$(date +%m%d%y)
./script /usr/tmp/file_name /usr/tmp/arch/file_name
[user]$ ls -l /usr/tmp/arch
-rw-rw-r-- 1 xxxxxx yyyyyyy 5 Sep 7 12:06 file_name_090718
#!/bin/bash
input=$1
output=$2
cp $input ${output}_$(date +%m%d%y)
$ ./script /usr/tmp/file_name /usr/tmp/arch/file_name
$ ls -l /usr/tmp/arch
-rw-rw-r-- 1 xxxxxx yyyyyyy 5 Sep 7 12:06 file_name_090718
