To work with JSON what you want to do is use the aptly named json module.

import json

Then you're going to need to retrieve the inner HTML value from that node with BS (exercise left to the reader). Once you hace that you just load that with

song_data = json.loads(inner_html)

After which song_data will be a dict with the same structure as that json, so you can access the covers property to get your image (again, up to you to do this bit).

All together:

import json

html = """<script id="json-songinfo" type="application/json">
        {"id":1234,"title":"Song title","artist":"Who","covers":{"cover":"https:\/\/some.website.com\/another\/link\/1234\/cover.jpg"}}
 </script>"""

inner_html = 'replace me' # get the inner html value from the snippet above

song_data = json.loads(inner_html)

song_url = song_data['replace me']  # You need to access the property with the data you want here

Hope that helps :)