From the Hertz website:
This is for the Denver-Downtown location which would be the closest location to Amtrak.
Hours of Operation: Mo-Fr 0700-1800, Sa 0700-1600, Su 0700-1400
Telephone: 303 297-9400
Address: 2001 Welton Street
Railroad- Meets Amtrak reservations during regular business hours. Pickup service is available, customer must call upon arrival.
Pick Up/Return Service
Available with a one hour advance notice and within 15 minutes from the Hertz Local Edition location. Contact the location to arrange for Pick Up service.
This is the information for the Amtrak Station Location:
Address: 1701 Wynkoop
Telephone: 303-297-9400
Hours of Operation: Mo-Fr 0700-1800, Sa 0700-1600, Su 0700-1400
RENTAL SERVICES PROVIDED BY:
Denver Downtown, 2001 Welton
There is not a Hertz counter at the station. Please call 303-297-9400, upon arrival to make arrangements for pickup service.
For other companies you might want to check their websites for Downtown Denver locations.
Hope this helps.