How do I use API key credential with Google text-to-speech client library methods?

Question

I'd like to instantiate a TextToSpeechClient() with an API key rather than service account credentials provided in a global GOOGLE_APPLICATION_CREDENTIALS variable. Specifically, I'd like to use the following function provided on the relevant website, but I'm unable to instantiate client due to lack of credentials.

def synthesize_text(text):
    """Synthesizes speech from the input string of text."""
    from google.cloud import texttospeech
    client = texttospeech.TextToSpeechClient()

    input_text = texttospeech.types.SynthesisInput(text=text)

    # Note: the voice can also be specified by name.
    # Names of voices can be retrieved with client.list_voices().
    voice = texttospeech.types.VoiceSelectionParams(
        language_code='en-US',
        name='en-US-Standard-C',
        ssml_gender=texttospeech.enums.SsmlVoiceGender.FEMALE)

    audio_config = texttospeech.types.AudioConfig(
        audio_encoding=texttospeech.enums.AudioEncoding.MP3)

    response = client.synthesize_speech(input_text, voice, audio_config)

    # The response's audio_content is binary.
    with open('output.mp3', 'wb') as out:
        out.write(response.audio_content)
        print('Audio content written to file "output.mp3"')

Alternately, I get past the credentials issue when I tried using the JSON from the Google text-to-speech website at https://cloud.google.com/text-to-speech and the requests package as follows:

r = requests.post('https://texttospeech.googleapis.com/v1beta1/text:synthesize?key=API_KEY', data = json.dumps(data))

and I receive a response with text content. If I was to do it this way, how do I save the content I receive as an audio file?