My google-fu also not doing well. Lots of great articles on ships from that era but very little on price. I think I'd have to hit the library. The quora response might be of interest, but it is mainly discussing merchant ships of that era:
Answer (1 of 3): This is a difficult question to answer since it depended on where the ship was made. However, it is possible to make a few educated guesses. Cost was largely dependent on where the ship was built, but at about £20 per ton could be considered average for a fully equipped sailing v...
www.quora.com
It offers a rule of thumb that would be useful to price ships: "an average of about £20 per ton could be considered average for a fully equipped sailing vessel. A 1100 ton East India merchant ship would thus cost about £22,000. A smaller vessel, such as the Bounty (ex-Bethia) cost about £4,400. The costs above are in 18th century £, so the cost today would be considerably higher with today’s currency values. The Bounty would have cost somewhere around £600,000 by today’s value, while the East Indiaman would have been a whopping £2.8 million."
Id.
Another quora response:
"A Dutch trading vessel of the type known as the Fluyt, was one of the most common merchant ships circa 1650–1750, they carried about half of all European shipping in this time period. A fairly standard price from the Hoorn shipyards was 10,000 Guilders. The average wage of a well off, but not wealthy, Dutch merchant was about 500 Guilders a year in the same time period. These Dutch cargo ships of 200 to 300 tons, were lighter built and faster then most British,Spanish or French ships of the time. They carried more cargo because they were not dual use merchant/ warships and had no gun decks. That also made them about half the price of a dual use merchant-warship."
Neither give any citations for where they are getting these prices.
Another quora posts does give cites to other online sources. Again, these are for merchant ships:
In 1770s, a merchant ship cost about £1000 in America:
Some Notes On Shipbuilding and Shipping In Colonial Virginia , by Cerinda W. Evans—A Project Gutenberg eBook
One hogshead (a large barrel of ~250 litres) of tobacco weighted ~1300 pounds or 585 kg, thus that ship's tonnage was about 220 tons.
Building ships in US was cheaper than in Europe (1790s):
Shipbuilding facts, information, pictures
Given that 1 dollar was equal to 0.22 pounds in 1790s, such a ship as mentioned above would cost £1700-2900 to build in England and £1200-1700 in US in 1790s.
Historical Currency Converter