I was trying to do a quest but they wanted Professor New Heartbreaker Cybernetic Bust Which is not available in shops. why have an item that a quest giver wants when we can't buy this. can the quests be tweeked?

Not all quests are meant to be doable. It will not be tweaked.

in my 5 months here and doing quests every day this has never happened

but it does happen.

Yeah, sometimes that happens. It's a quirk of any new item being released within a rarity Quests ask for, period.

It should ask for items that go lower in price. not something that is not able to be purchased

It's a brand new item that just got released; maybe it's not buyable now, but eventually it will be. Like Saturnine already said, it's just something that happens every now and then because the items that get asked for in Quests are based on their rarity, not on how many are actually for sale. You're asking for a fix, but give it enough time and this "problem" will eventually fix itself.

I'm sorry you had a little bad luck and a Quest asked you for an item that hasn't been around long enough to actually buy, but it's really not that big of a deal. Just cancel it and start a new one.

I think that I've read that, when it comes for new items being asked for in quests, the payoff is that you can sometimes receive brand new, valuable items as rewards. Drunk Carl sometimes gives out SubQ items when he sleeps, so you have a slim opportunity of getting those--just like there's a slim opportunity for a quest-giver to ask for those items.

You can be either super lucky or super unlucky; that's just kind of how quests go. Ultimately, one missed quest isn't going to make a massive difference in how much sP you earn in the long term, so I doubt quests will ever be adjusted to not ask for newly-released items.