Nope!
In general ring tones are generated by the calling party's switching equipment. There is an exception to this that is exploited by ring-back tone provider equipment. The exception was originally provided to allow PBX equipment to provide busy/ringing/reorder signals.
I've looked at both AT&T (mobile and wireline) and Verizon (mobile only) ring-back tone products and both allow the subscriber to set specific ring tones for specific callers.
The person you are calling must be convinced to change their settings to accommodate your wishes.
I'm pretty obnoxious about my ring-back tones. My boss hears Janice Joplin belting out "Oh Lord won't you buy me a Mercedes Benz..." Special for him only.
Ever consider that your calling party might be messing with your head for grins?
Ever consider that ring-back tones are part of a person's fashion ensemble? Asking them to turn off ring tones might be like asking someone to wear different colored shoes.