Gold has a density of 19g/cm^3.
Let's say the interior of the chest has a volume equivalent to 40*40*50cm. That's 64000 cm^3.
Let's say 3/4 of the interior of the chest is gold. The rest is air. So that's 48000cm^3 of gold.
48000cm^3 * 19g/cm^3 = 912000g.
So your pirate chest would weigh about 912kg, give or take 510 kilograms of wood and other metals in the chest itself, provided the gold coins were pure gold. (24k) They usually weren't; other metals were mixed in to make the coin more durable.
England still uses the "crown gold" standard for minting new gold sovereigns. It was introduced in the 1500s by Henry VIII, I think, so I guess that could be the type of gold crown reasonably expected to show up in a pirate chest. Crown gold is 22 karat (91,667%) gold, with the rest strictly copper. Copper has a density of about 8,96g/cm^3. Roughly, that would decrease the weight of the chest by about 4%.
So the chest would weigh in at about 875 kilograms. Or about 1930 pounds. Man, gold's heavy.
(Apologies for any mistakes  I just came off night shift and I'm going crosseyed.)
