how to add a coroutine to a running asyncio loop?

You can use create_task for scheduling new coroutines:

import asyncio

async def cor1():
    ...

async def cor2():
    ...

async def main(loop):
    await asyncio.sleep(0)
    t1 = loop.create_task(cor1())
    await cor2()
    await t1

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