First off, I'll start with a list of figureheads (in order of usefulness) - Seahorse, Commodore, Unicorn, Lion, Giant Eagle, Hero, Neptune, Dragon, Angel, Goddess. The first 8 are available almost everywhere (although there are a few ports I've noticed do NOT have the Dragon until you are able to get the Angel or Goddess).

And a list of guns (also in order of usefulness) Saker, Demi-culvern, Culvern, Cannon Pedero, Demi-cannon, Cannon, Carronade. The first 6 are available at any shipyard, and since there's only one special type of gun, it seems easier to get than the Goddess figurehead.

Ok, now to the questions of where and how to get them...

I know for a fact they are available in Venice, Hamburg, Antwerp, and Athens. so I have reason to believe they are available in ANY non-capitol shipyard.  However, there are a few things you must do to be able to purchase these elusive Angel and Goddess figureheads.and Carronades for guns.

1) The industry level of the port must be 1000. (This in and of itself makes getting them at capitol cities impossible since you cannot invest in the shipyards there)  Some have speculated that having the economy of the port at 1000 helps...  I can say I've personally bought Angel figureheads and Carronades when the economy was in the 900's ... So, it may require the economy to be 1000 for the Goddess.

2) Your character's luck must be at the max.   (THIS is what everyone groans about :)  ...  Luck is an unseen attribute of your character but you can judge it's level when you go to a fortune teller and ask about 'Life'   I'll explain how to increase your luck in a bit.)

3) YOU (meaning the player) must have patience.  Even if the above factors are correct, they are NOT available 100% of the time.  You have to keep bugging the shipyard worker until he says "We have a great selection today." (or something similar)  And even then, most of the time he will only offer the Angel... so keep bugging him until you get the Goddess.

Now onto how to increase your luck.  There are disputes about the actual method, but the root action is the same.  Donate money to the church or mosque (PC version) or Round Earth Society (SNES and Genesis versions).  The actual amount of money you donate is not as important as the PERCENTAGE of your cash on hand you donate.  Luck also fluctuates throughout the game so you may find that you have to donate money at more than one stage of the game to keep your luck at 100.

I conducted the following test in the SNES version (with an emulator, since I know which memory address was the 'Luck" for the character I was using I could check and modify it's value)  ...

If your luck is:   ...  The fortune teller will say:

0 - 24     "Oh. I see an ominous shadow across your face. You may be doomed to have a difficult life."
25-49    "Your fortune doesn't look very bright.  Be careful, and watch out for accidents."
50-74    "You have an average fortune.  But remember, you are the one who carves your own destiny."
75-99    "You have a good fortune.  Have more self-confidence."
100        "What a strong fortune!  You have nothing to fear in this life."

Quotes are from the SNES version. They may not match exactly in the PC version (although I think they are the same as the Genesis version). And remember, your luck should be at 100 to "unlock" the special figureheads and guns.  If anyone out there knows the exact quote from the PC version please email me and I'll include it  the next time this comes up.

I also tested different percentages and charted the luck increase.

I started with 58 luck and 1,000,000 gold on hand.  (easy number to work with percentages) donated an amount, noticed the increase and then reloaded the game for the next try. (Again, this test was on the SNES version on an emulator, I make no claims as to how it will work with the PC version)

Percentage of
Cash on Hand
donated                         Luck increase
----------------------------------------------------
Less than 10%           -   None
10%                             -  1 point
11%                             -  2 points
12%                             -  3 points
13% - 14 %                 -  4 points
15% - 16%                  -  5 points
17% - 20%                  -  6 points
21% - 25%                  -  7 points
26% - 33%                  -  8 points
34% - 50%                  -  9 points
51% and up                 -  10 points

This is in NO way a comprehensive test. Results may vary. But I hope this helps.