Conical features are frequently used in tool holders and on self-aligning tools, and are completely valid as datum features. Put the datum feature callout on the conical surface or on a leader extending away from it. A cone actually produces a datum axis and a datum plane; this gives you three mutually perpendicular planes to work from. The first two planes result from the axis...no surprise there...the datum plane (the third plane) is located at the vertex of the cone. The vertex is a useless point because you can't stabilize anything there, and often doesn't physically exist because the cone is truncated. To get around this automatic generation of the secondary datum plane (the third plane), you may need to clearly specify a limitation/exclusion on the drawing.
Assuming that you want the axis to be the primary datum feature, select the conical surface as the primary datum feature and include a note under the datum callout (or in an addendum or note elsewhere) indicating that the axis is only being used to generate the primary datum (axis); then label another feature as the secondary datum. In the FCF, include the primary datum and secondary datum (and tertiary as needed to clock the part).
It's easier if the cone's axis can be the secondary datum; the primary datum will already override the datum plane that would otherwise have been generated at the vertex.
Another option, rather than using the entire surface of the cone is to use a series of datum targets. A ring (usually 5 points MIN to catch lobing effects) of targets at a location near one end of the cone and a ring (an odd number of points, but more points than at the first ring) of targets near the other end of the cone will be used, with the RESULTANT axis being used as the datum. (Note, the RESULTANT axis DOES NOT correspond to the actual axis of the part).
Another option that I've heard of is to use a toroidal ring to locate the center at one location (essentially line contact) on the cone, and a series of 3 or more (odd number again) points around the circumference at a substantial distance from the toroidal ring. This method actually sets up a compound-datum which, of course, may have nothing to do with the actual axis of the part.
My preference is to specify the whole surface to generate the axis, and meet with inspection to agree on a mutually-acceptable way of establishing the datum in practice (and document it!).
Sorry it's a long answer, but it's a major topic! Hope it helps.
Jim Sykes, P.Eng, GDTP-S