I don't work with these terms. I had to look them up. However, understanding what they mean, I can say what I think I would expect, partly informed by what I've read during research.
Firstly, FOB appears to require qualification. In international terms, it needs a port specifying. If that's a port of embarkation for the goods, it means that the seller's responsibility and liability ends once the goods are loaded at the port. If it's a port where the goods are unloaded, the responsibility and liability pass to the purchaser once the goods are unloaded. However, you might know better than me whether there is a common shorthand when the port is omitted.
I wouldn't actually expect any preposition in this case. "I bought these FOB (port)" would seem most natural. If a preposition is really needed, I guess "as" would be appropriate. The same would apply to CIF, though "with" would make sense there based on expanding the abbreviation.
It seems that various reliable sources (such as the UK government) do consider letters of credit a form of payment, presumably because they are guaranteed. However, I would think that would be phrased "upon payment by letter of credit", or "on receipt of a letter of credit". Payment methods are usually handled in that sort of context as "payment by method".
I'd never heard of "payment during delivery" before, and a quick Google doesn't find much for it. What it does find would seem to mean the same as "payment on delivery", or sometimes "cash on delivery". Which preposition (if any) you would use there would be heavily dependent on the overall sentence.