I recognize this is probably going to vary massively depending on exactly which ship we are talking about, so perhaps we could get a multi part answer here.
1.) If you look at the classic ship of the line, such as Nelson's HMS Victory, you will find over 100 guns on her throughout three gun decks as well as smaller armaments on the main deck. The physical space alone for the gunpowder and cannonballs must have been massive. How many times could this ship, or one similar, probably do a full broadside before running dry?
2.) A smaller ship, but still very capable, the HMS Surprise as seen in the movie Master and Commander, has 28 guns. Same question as above really. Does the amount of ammunition scale down at a 1:1 ratio? or does a smaller ship with fewer guns carry more or less ammunition?
3.) much smaller this time: a privateer in a 4 or 6 gun sloop. Would privateers or lightly armored ships with few guns carry enough shot for a few "harassment" engagements, or would it also be able to sustain fire?
Arrangements for shot and powder varied over time, but an early C19th table of stores shows 93 cartridges and shot for each of the lower deck guns, 105 cartridges and shot for each of the middle deck guns and 114 cartridges and shot for the guns on the upper deck and gaillards (and for the carronades of the larger vessels). Powder supplied for guns in a mix of 1/3rd 1/4tr and 1/6th shot weight charge bags (mostly unfilled, with powder in barrels (~90lbs each) to fill them - and in a proportion which approximates an average of 1/4tr of the shot weight, plus a little bit 'spare').
The frigate only has upper deck and gaillard pieces with 114 rounds each... but the smaller brig or cutter has reduced space and weight capacity to carry closer to 90 rounds for each gun. A merchant would dedicate less of it's space to guns and shot and powder, would practice less often - but the minimums required by insurers or by the Transport board were 6 guns of 6pdr or more (or less according to her tonnage), or 12pdr carronades or larger, with ~30 rounds per gun. An incentive of £5 per gun was offered by the transport board as an incentive to carry more guns for self protection.
The supply from that table of loading is made up of mostly roundshot, with these loadings being for foreign service - home fleet service had 30 fewer roundshot and less powder - the Lower deck guns for home service carry only 3 grape shot, and no case shot with 60 round shot. The middle deck guns 5 grape shot, no case shot and 70 round shot. The gaillard and upper deck guns 7 grape, 7 case, and 70 roundshot - where fewer shot are loaded these are reduced in the home service round-shot for less capacious vessels.
Later ships reorganised their stowage to allow shell rooms for explosive spherical shell, and provide shot for larger bore ordnance - which was permitted by an improvement in accuracy and consistency in practice, with sights, heavier shot etc - but reduced to 80 rounds per gun (mostly 32pdrs throughout, with some 8" shell guns and 68pdr pivot guns in some cases) - with carronades carrying ~50 each (with an option to load more if sufficient space can be found, up to 80 rounds. Those guns designated as shell guns might use roughly half and half shot and shell, with less dedicated to grape or case.
French tables of loading are similar, if not identical, with ~100 rds for lower deck and middle deck guns, 103 or 110 for upper deck and gaillards pieces, with their carronades supplied with 77 or 87 rounds (if they match or differ from the calibre of other artillery). Their smaller vessels carry 85 rounds for guns on their weather deck and gaillards, and 72 or 82 rounds for carronades. The espagnoles and perriers were supplied with 75 rounds. Part of this supply was for exercise and practice, and part for combat service.