[sigilis]

You would assemble such a craft in orbit. Some of the proposed designs for nuclear pulse propulsion conceive of a spacecraft of truly astounding proportions. The wikipedia article on Project Orion mentions an Alpha Centauri bound design that would be 20km in diameter and 10Mt in mass.

However, now that I think about it, cyclers would only need to use the NPP engines (bombs) to get into their cycling orbits, so you might be able to get away with accelerating them while unmanned. You could design such a craft with much less radiation shielding, but still include enough to prevent cosmic rays from killing (or more accurately, increasing their cancer risk) the passengers giving such a craft a significantly larger fraction of usable mass for other purposes. Initially accelerating a Mars cycler with unmanned landers with supplies and materials for an initial colony with humans to follow could be an interesting design.

All of this is more expensive than anyone is willing to pay for, even if there was an appetite for the nuclear proliferation risk of making and then putting a thousand compact bombs on a spacecraft. Not even mentioning the risk of the bomb carrier rockets exploding and causing a 100x Broken Arrow situation.

It is for this reason that I must urge the government to immediately fund the writing of several novels about how this can go wrong and right for me to read.