Pasdar,
While I too have no such register, I can pretty reliably identify most solid-fuel ballistic missiles built in the last 30 or so years off hand (especially Soviet/Russian and Chinese systems).
And I never said such a thing was impossible simply that I don't think it has ever been done for whatever reason.
For example, China's first fairly modern solid-fuel ballistic missile was the DF-21/JL-1 (which are one in the same missile) back in the 70's and 80's had two stages and a range of only 1700km in the original models.
However there is one missile I can think of that could give us a hint at what much a missile would look like, the MGM-134 Midgetman ICBM.
This "tiny" ICBM was just 14 meters long, with a diameter of 1.17 meter, weight just 13.6 tonnes, and has three stages. Yet as small as this missile is..It had a range of 8000km! So logically speaking, with the proper solid rocket engine technology, one should be able to design a single stage missile with just a quarter that range.