Asking someone for their cheerful price is asking them for the price at which they'd certainly do what you ask.
This opens the door to asking for whatever you want. Prostitution, murder, watching 'The Bachelor' on loop for all your waking hours for a year: what is your cheerful price? The answer may easily be 'I don't have one,' because my emotions can't always be indefinitely swayed by money.
This is easy, though. The harder problem is being asked your cheerful price for something you would be willing to do for money, but where the transactions costs, risks, and trust issues prevent you from negotiating it.
If you ask me my cheerful price for writing a software program, not just the work but my professional reputation is at stake. You might use your cheerful price request to justify asking me for things I'm very reluctant to do, and wouldn't do at a fair or market price.
If your service request is under-specified, you really need to ask my cheerful price to negotiate my cheerful price. How do I know you won't complain to others that my quoted price was unprofessionally high, neglecting to mention and explain that we'd agreed to a cheerful price? What if you keep inflating quality and scope demands after I commit to turn my cheerful price into a merely fair price?
You need enough of my trust in advance for me to be willing to quote you my cheerful price. I need to structure a cheerful price in a way that defends my reputation and accounts for the risk you'll say 'no,' in which case I'll have wasted my time coming up with the offer. These issues can make being asked for a cheerful price feel strangely uncomfortable.
I propose an alternative, the 'cheerful bid.' The one who wishes to pay a cheerful price comes up with a proposal of what they'll pay to cheerfully negotiate a 'cheerful price' for a product or service, with full freedom for either party to walk away from the negotiation at any time.
Here's how it might work:
Alice: Hey Bob, can I pay you $0.25/minute to negotiate your cheerful price to write some software for me?
Bob: What kind of software?
Alice: Careful, Bob, you just worked for free! I want to know if you'd accept $0.25/minute, potentially for several hours, to discuss that with you. During that negotiation we would try to find a price I am willing to pay, and you would feel delighted to accept.
Bob: Sounds weird, plus I barely know you, plus I have a lot of serious fair-price offers that I place higher trust in. I don't think $0.25/minute is enough to get involved in a negotiation I don't really understand.
Alice: I get it. What if I Venmo you $100 in advance right now just to show I'm serious, and I'll pay you $1.25/minute just to negotiate with me, no strings or obligations attached?
Bob: Sounds good!
Alice sends him $100 and they make plans to negotiate Bob's cheerful price.