➜ python methodtests.py 
methodtests.py:18: RuntimeWarning: coroutine 'TestClient.request' was never awaited
  async with client.request(method, url) as resp:
RuntimeWarning: Enable tracemalloc to get the object allocation traceback
Traceback (most recent call last):
  File "methodtests.py", line 43, in <module>
    loop.run_until_complete(main())
  File "/home/nick/.pyenv/versions/3.7.2/lib/python3.7/asyncio/base_events.py", line 584, in run_until_complete
    return future.result()
  File "methodtests.py", line 40, in main
    await check_client(client, "/")  # XXX dies
  File "methodtests.py", line 18, in check_client
    async with client.request(method, url) as resp:  # YYY dies
AttributeError: __aexit__

import asyncio
import aiohttp.test_utils
import aiohttp.web

async def handleall(request):
    return aiohttp.web.Response()

async def check_client(client, base_url):
    for method in ["GET", "POST", "PUT", "DELETE"]:
        url = base_url + method.lower()

        # slightly awkward, but works with both client types
        clientmethod = getattr(client, method.lower())
        async with clientmethod(url) as resp:
            assert resp.status == 200

        # fails with test clients
        async with client.request(method, url) as resp:  # YYY dies
            assert resp.status == 200

async def main():
    # a "regular" ClientSession
    base_url = "https://httpbin.org/"
    async with aiohttp.ClientSession() as client:
        await check_client(client, base_url)

    app = aiohttp.web.Application()
    app.router.add_route("*", "/{verb}", handleall)

    async with aiohttp.test_utils.TestServer(app) as server:
        async with aiohttp.test_utils.TestClient(server) as test_client:
            base_url = str(test_client.make_url("/"))
            # a "regular" client created from the test client
            client = test_client.session
            await check_client(client, base_url)

    async with aiohttp.test_utils.TestServer(app) as server:
        async with aiohttp.test_utils.TestClient(server) as client:
            # just the test client
            await check_client(client, "/")  # XXX dies

loop = asyncio.get_event_loop()
loop.run_until_complete(main())