Unconfirmed BTC transaction / TXID doesn't exist? I recently tried sending some btc to coinbase.  In a hurry I did not put a transaction fee.  I've tried to explain to their customer support what is going on.  I offered to charge me a fee through my wallet on coinbase to do a pay for parent protocol. Their lack of understanding is making me worry.  I tried using ViaBTC.  I put in the transaction ID and they said the TXID did not exist.  Any suggestions would be appreciated.  Its approaching 7 days now.  Thank you.
In any case, receiver (Coinbase) can't do much to make your transaction confirm faster. Except CPFP, but you can do the same with your change output, if you have it. But, as mentioned above, if tx fee really is 0, it will not be relayed by the network, as default relay fee is 1 satoshi per vbyte. Also, in 7 days it should have been confirmed, as mempool clears out regularly at the moment. I bet you will not see that transaction by txid in any public block explorer either. So, you should just send them again from the wallet you initially send them out.