I can't use normal tools and technics to measure the performance of a coroutine because the time it takes at await should not be taken in consideration (or it should just consider the overhead of reading from the awaitable but not the IO latency).
So how do measure the time a coroutine takes ? How do I compare 2 implementations and find the more efficent ? What tools do I use ?
If you only want to measure performance of "your" code, you could used approach similar to unit testing - just monkey-patch (even patch + Mock) the nearest IO coroutine with Future of expected result. 
The main drawback is that e.g. http client is fairly simple, but let's say momoko (pg client)... it could be hard to do without knowing its internals, it won't include library overhead. 
The pro are just like in ordinary testing:

it's easy to implement, 
it measures something ;), mostly one's implementation without overhead of third party libraries,
performance tests are isolated, easy to re-run,
it's to run with many payloads
How to measure Python's asyncio code performance?