Vee blocks will easily crush tubing etc. if used in a vise.
For low /medium production work usually I use aluminum soft jaws in the vise and after placing a spacer between them I will bore at two places a few thou oversize so as to accept 2 workpieces per station
--If I do this with 3 double lock vises on the table this nets me 12 parts per cycle.
One possible solution flat round is what is called a finger plate or finger vise. Nowadays these are generally shop made.
If for end working, your best solution may not be a vise [in the usual sense] at all, but rather a substantial slotted right angle iron, with "pinch" clamps or cotters you can make yourself. Drawback is that you will need a different clamp or cotter for each diameter, but you can accommodate tapered or threaded stock and machine the pinch clamp* to a larger size to reuse. It is also easy to set up accurate and repeatable angles. Magnetic sine bars are best [most accurate and easiest to use] , but a good protractor is generally adequate for home shop projects.
* avoid the temptation to use a set screw. These will generally mar the work and don't hold as well as a good close fitting pinch clamp or cotter. Most of the mail order mill supplies should have angle irons in stock. Get one that is about max for your machine. For some examples see
-- Unka George (George McDuffee) .............................. The past is a foreign country; they do things differently there. L. P. Hartley (1895-1972), British author. The Go-Between, Prologue (1953).
I'm not a machinist, but the first obvious answer is the v-blocks; but if you're holding something delicate, you could conceivably make a pair of jaw inserts with semicylindrical notches that match the OD of the part.
My 2 larger screw less vises both have V cuts in one jaw that work fine for most round objects. Actually two V cuts. One horizontal and one vertical. This allows my to mill on the end of a small round object or square off the end of a long piece of tube or rod.