At this point, you've received a counter offer based on the original negotiation letter you sent the employer.
The original proposals were:
The employer has come back with a counter offer:
The employer has explained they can't deliver the onsite parking. The real issue, now, is that $20,000. Unfortunately, you can't afford to ignore that. You need to get at least part of the difference, somehow.
Negotiations have to work on what's doable, as well as what's needed.
The short answer here is to split the difference in salary, and go for something around $130,000. It's obvious, and in fact may be what the employer intends, by making that offer. Holding out for what may be an impossibility isn't good for anyone. It's a waste of time.
If there's a counter offer, the bandwidth is also much smaller, and you're making progress upwards from $120,000, not downwards.
At this point your letter needs to be brief, courteous, and to the point.
You should leave yourself some room to maneuver.
You don't have to give up on trying to get a better deal. You do have to acknowledge the employer's offer and reply realistically to the proposal. If you go straight down to $130,000, the counter offer will be $125,000 if the employer uses the same logic.
The example allows room for negotiation:
Addressee (Signatory of job offer letter or appointed negotiator, if applicable)
Thank you for your prompt and positive response to my letter regarding the (position title) job package. I very much appreciate your efforts and your willingness to meet my needs for the day care and holiday components.
I'm sorry to say that the remuneration issue remains to be resolved. I've done some calculations, and I find that I can accept a salary of $134,000 instead of the original amount. I'm still restrained by my basic obligations, however, from accepting a significantly lower amount.
I think we can finalize this matter easily, if a mutually acceptable solution can be found.