A way to describe a group of trees of one species using only one word
You can't say this in one word.
While it is difficult to prove a negative, I believe there is no general one-word solution that works for every species of tree. For particular species, you might find a particular single word solution.
To be honest, I'm not sure why you would want to use one word rather than several; your answer doesn't make that clear. Were I you, I'd be happy with an oak thicket, an oak stand, an oak grove, an oak copse, an oak wood, an oak forest etc. as they are no less expressive than any single word equivalent that you might hope exists!
In your comments you mention pinery. A quick dictionary search shows that oakery does not exist and neither does birchery; hence it is not a general solution. Also, pinery is not a particularly common word, and I doubt it could be used for a pine forest, for instance.
-wood as a suffix
As for your suggestion of using -wood as a suffix, that just doesn't work. It's unreliable.
Were you to consult a dictionary, you would see that it is not the case that in every instance a tree name concatenated with wood gives the name of a group of trees; more usually it is just a type of wood, in the lumber sense.
While Merriam-Webster has birchwood as both a material a carpenter might use and a birch wood i.e. many living birch trees still stuck in the ground, the same is not true with oak. In this instance, according to Merriam-Webster, oakwood is only the material and not the collective body of trees; similarly, cherrywood, and applewood are materials only. Ashwood and rowanwood do not appear to even exist as compound words. (Perhaps they are not practical for carpentry or arboreal monoculturing... I have no idea!)
I'm not sure to what extent the -wood suffix is generative and whether there is any rule as to when it creates woods as well as plain old wood. Perhaps some linguist has investigated this, and a knowledgeable answerer will let us know. (However, it is probably just entirely irregular.)
Edit
The question was edited in a significant way after I answered, which makes the above answer less relevant.
Coppice can refer to a single-species wood or grove when it is vegetatively propagated. (A coppice could even be a grove or a small circle of trees where each plant is a clone of one mother tree.) As a transitive verb, coppice refers to a traditional forestry/pruning technique which results in the formation of coppices in the nounal sense.
Coppice is clearly a cognate with copse and it can be used with exactly that meaning. However, when this more unusual and awkward spelling is used, it is typically with the more specific, necessarily single-species meaning.
In its limited sense, coppice does not, however, refer to any single species stand or wood of trees; the clonal means of reproduction is what makes it a coppice.
Merriam-Webster gives the following definition:
coppice noun
Definition of coppice (Entry 1 of 2)
1 copse
2 forest originating mainly from shoots or root suckers rather than seed
an oak coppice
coppice verb
coppiced; coppicing
Definition of coppice (Entry 2 of 2)
transitive verb
to cut back so as to regrow in the form of a coppice
intransitive verb
to form a coppice
specifically, of a tree : to sprout freely from the base
You can say ‘a stand of trees’ such as ‘a stand of birch’ - a ‘stand’ means a group of the same type of trees. But there is no single word as far as I know. And you cannot say ‘oakery’ etc. So you can say ‘he stopped near a stand of birch’. You do not need to say ‘trees’.