Not sure what you are asking, Lllinda. Any stem of the suitable size and age can be used as a cutting. Cotoneasters are twiggy shrubs, however--there is no main stem, as such.

I'd say it depends what type of cuttings you want to take eg hardwood or semiripe?

Some Cotoneasters are trees, so they do indeed have a main stem, Tug, as do some of the larger shrubs.

Well, when someone talks of a "main stem" in plants, I think of either a central leader, as in many large forest trees--Spruce and Firs are extreme examples--or the main flowering stem in many annuals or biennials, such as Foxglove or Hollyhock. "Main stem" could also mean the trunk of a tree, but propagating from the main trunk?? Give me a break! It's a pretty meaningless term otherwise. I asked my question to get enough information to imagine just what it is that Lllinda wants to do.

Just select a shoot of semi ripe wood, ie a shoot that grew this year and is half way to hardening off.
Actually they are very easy to grow from seed if you have some.

Usually cotoneaster trees are topworked , grafted onto a strong standard stem
The top of ours died and we cut the trunk low, rather like stooling, its now a big strong bush, taller than me and wider than my outstreched arms
Semiripe cuttings sre easy as Stera says.......fun to grow from seed too, takes longer

Ah, a grafted Cotoneaster standard. As Pamg said, the trunk is going to be a different variety, so cuttings taken from the shoots growing off the trunk will be quite different from cuttings taken from the crown. Neither is going to reproduce what you had before.

...if it is in fact a grafted standard.

True, but that fits the phraseology of Lllinda's question. It would be nice if she could get back to us and confirm it, though.