I thought I typed a response earlier but it seems to have disappeared.
I fear you are asking, in large measure, for the unobtainable - not that you shouldn't ask. I'd love to give specifics but I have found that such information is really hard to come by. For a simple example, look at the Wikipedia orders of battle for Monmouth and Brandywine. While there is information for artillery in both, it is mostly in broad strokes with very little information on specific pieces. And as to the units, you may get 4th regiment for the British or such and maybe something similar for Continentals but, at least within my experience, it is rare to get anything more specific than that. And, yes, Wikipedia isn't necessarily the best source - but isn't the worst, either.
But I'll give this much, for the British, I'd paint units of the 4th regiment, with some in tricorns and others in helmets. And since there wasn't much to differentiate between the different British artillery regiments, you're pretty well covered for British regulars. And I do believe the majority of the regular artillerists were from the 4th regiment. I have a memory of a thread on TMP where someone did mention that there was at least one distinguishing characteristic for one of the other regiments, I think it was a white feather - might have been for the 1st regiment but I wouldn't bet any money on that. Otherwise, all the regiments of artillery were essentially in the same uniform (or maybe there were differences but too subtle for the scale of our miniatures, whether yours in the larger or mine in the smaller). I'd guess you could paint some units in floppy hats without anybody being able to document that wasn't correct given how many adaptions were made to the warranted uniform guidelines.
You might have better luck with German units. I would be shocked if you don't already have a copy of Mollo's book on AWI uniforms with its numerous illustrations of artillerymen for most sides - sorely lacking on anything for the Spanish. If you want to go down the Spanish route, this is the best source I've found to date:
http://www.uniformology.com/WORLD-10-SPN.html. I'm pretty sure there is information for Spanish artillery in that mix.
Your best bet - and maybe some respondents here will have that information more readily to hand - is to dive into books on specific battles in the hopes that you get more detail for that specific battle. Again, I fear such information to be scare; not non-existent, just scarce. I'd love to be proven wrong if someone can reference better sources.
I shall watch this thread with great interest because this is an area I'd love to have better information about.