That's true, but the DM might allow a success on a lower roll than a nat 20 if the character roleplays well, ie. Not just a shoulder touch and a wink.
I would come in with some kind of appeal to the dragon's vanity, maybe talk about how there is some kind of great trouble in a nearby kingdom and claim to be emissaries of the king and offer a considerable amount of wealth to add to their hoard if they help to protect the nearby kingdom. Then try to hash out the terms of the deal, which should be distracting enough.

Inorthstar is right, you gotta fuck that dragon. Rules are rules.

Damn

Thanks guys! Guess it's time to get my sexy on

If you want to go with a non meme approach, try stroking the ego instead of the dick. Bilbo did that, and he didn't turn out extra crispy. Irredgardless of your approach, if you have any background information on the dragon, try turning that to your advantage. Does the dragon really want to fight? Could it instead be bought/distracted with a hefty chunk of treasure? What has this dragon achieved that it is particularly proud of, or be convinced to be proud of? Could you claim someone (i.e. another big bad) else sent you here to end the dragon? All in all it might be best to try talking before your party starts slinging spells and swinging swords, since it might not want to keep a conversation up in the middle of combat, but that could turn out to not be the case.

@tarotnathers13th "...try stroking the ego instead of the dick" lmao I'm dying!!! Thank you for that bit of genius

@tarotnathers13th that is the approach I was going to try and go for however I am not as eloquently spoken as my charcter is. But that is very good advice. Thank you so much

The Hobbit would have been a much different film if Bilbo had stroked the dick instead if the ego

XD

Either way, I'd like to volunteer to roleplay said dragon haha

Now you have to tell us how it went?

Oh yeah, keep us updated!

The session got canceled but I'll let you guys know for next week wednesday

Ok so an actual technical look at this. Black Dragons are described as solitary and territorial and don't like other beings being around in general so the servitude thing is probably not a good idea. Your best bet as a prompt is convincing it you will leave and never return.
Also someone said you could roll a nat 20 and work off it. Persuasion would be a skill check. There are no Nat successes on skill checks so don't rely on that.
Now I mostly play Pathfinder not DandD but as far as these rolls go in Pathfinder, he would be starting out as hostile by default, Meaning you would have to make multiple successful rolls. In DandD I'm assuming it would be a roll with disadvantage.
Unfortunately you seem to have run into probably one of the hardest kinds of dragons to persuade or bluff. Unless your DM is homebrewing this dragons attitude you might want to rethink your options. It being an "Old" dragon, unless you're high level the best option is probably run.

Holy shit that is amazing advice. Thanks so much
I'll definitely check with the dm before hand and see/or otherwise just the rest of my party

So we all survived!! But the dragon got away with the egg. We were so damn close to escaping with it but alas
Now we've all leveled up and there's a massive fucking army right outside he cave we're in so we're gonna have to fight for our lives. BUT my Dancing Great sword is finally attuned [not as cool as I thought it would be but that's okay] and I've got some very fun new spells. I'm looking forward to using Animate Objects so damn much

Do you play online? A friend of mine is in this group that plays online and they stream the gameplay and the entire experience just felt different to me. Maybe it was just me in an observable perspective.

Nah I play with a group in person. But I've heard online is fun too

Glad you got out safely. My group is at the finale of rise of the runelords and knowing what the final boss can do I'm not sure we're gonna make it

Then may they die valiant deaths!