I guess you can get that Great Merchant who gives 3 oil per turn is it?
Yes, the Rockefeller feller. 3 oil per turn for a poor man's oil powered army.
Here comes also all these situational tricks, that you might, just
might have an opportunity to use in a game out of many, like, becoming Suzerain of oil rich CSs, culture bombing those just over the border resources when respective Congress resolution is in force (a lot of stars must align for this one), or culture flipping oil rich border cities.
At times if I play too slow and peaceful I can't get Oil Units for War which bothers me.
Yes, better do your war before oil units. Then either you will not need to do any more war when oil era comes and by some miracle you're completely out of oil, or you'll have enough of it to keep firing those well oiled projectiles.
But if you play peacefully in the beginning, you can just continue to do so in oil and further eras. The ink on all those declarations of friendship is mighty strong, makes oil totally irrelevant.
<...>1 unit per Trade<...>
Tedious but better than not having Oil.
Go on and trade like 80 units one at a time per trade session. You'll need to rinse and repeat this grand trade operation a few times per game. Then come back and tell me, if you still think it is "better than not having Oil".
After one such game my view went to a radical "screw it, I'm not doing that again".
And if tediousness and terrible user interface still do not discourage you, you can also sell your strategics to AI, especially the ones who are at war - that might keep them at it a little longer. For selling, they take two or even three units at a time without starting to drop the price, so it goes a little bit faster than buying. If you sell by 10, you'll lose a few coins.
But they will buy up until 21-22 - a full unit price plus a small reserve not to be out of resource and be able to heal, I guess. Or was 41-42, now I can't remember if it was different game speed. Experiment and see for yourself. And yes, Concise UI mod and especially its improved deal screen will somewhat cut the tediousness down.
Still, FXS could review the algorithm. 7 gold for one unit, and your entire empire including the shirt off your back for a batch of 20 units, but only 140g for the batch equivalent, if bought one by one. Come on...