Coroutines are built on iterators - the __await__ special method is a regular iterator. This allows you to wrap the underlying iterator in yet another iterator. The trick is that you must unwrap the iterator of your target using its __await__, then re-wrap your own iterator using your own __await__.
The core functionality that works on instantiated coroutines looks like this:
class CoroWrapper:
    """Wrap ``target`` to have every send issued in a ``context``"""
    def __init__(self, target: 'Coroutine', context: 'ContextManager'):
        self.target = target
        self.context = context
    # wrap an iterator for use with 'await'
    def __await__(self):
        # unwrap the underlying iterator
        target_iter = self.target.__await__()
        # emulate 'yield from'
        iter_send, iter_throw = target_iter.send, target_iter.throw
        send, message = iter_send, None
        while True:
            # communicate with the target coroutine
            try:
                with self.context:
                    signal = send(message)
            except StopIteration as err:
                return err.value
            else:
                send = iter_send
            # communicate with the ambient event loop
            try:
                message = yield signal
            except BaseException as err:
                send, message = iter_throw, err
Note that this explicitly works on a Coroutine, not an Awaitable - Coroutine.__await__ implements the generator interface. In theory, an Awaitable does not necessarily provide __await__().send or __await__().throw.
This is enough to pass messages in and out:
import asyncio
class PrintContext:
    def __enter__(self):
        print('enter')
    def __exit__(self, exc_type, exc_val, exc_tb):
        print('exit via', exc_type)
        return False
async def main_coro():
    print(
        'wrapper returned',
        await CoroWrapper(test_coro(), PrintContext())
    )
async def test_coro(delay=0.5):
    await asyncio.sleep(delay)
    return 2
asyncio.run(main_coro())
# enter
# exit via None
# enter
# exit <class 'StopIteration'>
# wrapper returned 2
You can delegate the wrapping part to a separate decorator. This also ensures that you have an actual coroutine, not a custom class - some async libraries require this.
from functools import wraps
def send_context(context: 'ContextManager'):
    """Wrap a coroutine to issue every send in a context"""
    def coro_wrapper(target: 'Callable[..., Coroutine]') -> 'Callable[..., Coroutine]':
        @wraps(target)
        async def context_coroutine(*args, **kwargs):
            return await CoroWrapper(target(*args, **kwargs), context)
        return context_coroutine
    return coro_wrapper
This allows you to directly decorate a coroutine function:
@send_context(PrintContext())
async def test_coro(delay=0.5):
    await asyncio.sleep(delay)
    return 2
print('async run returned:', asyncio.run(test_coro()))
# enter
# exit via None
# enter
# exit via <class 'StopIteration'>
# async run returned: 2