growing under olive trees that are in tubs

I'm looking after a place that has 3 youngish olive trees in half wine barrels. I'd like to grow some leafy edibles over the winter in the tubs, but am not familiar with olives at all. The olives have been fed coffee grounds in the recent past (will that have made soil acidic? There were a few sheeps sorrel plants growing there). I'm planning on adding an inch or so of wormcastings/compost mix on top of existing soil and growing in that. Not sure what will happen with the pH in the tubs, or if I should do anything about it.

The tubs are on the edge of a verandah so will get watered off the roof on one side when it rains (650ml/yr), giving a drier side of the tub and a wetter side. We have up to -10C frosts during winter (most less than that), very occasional snow. Other wise sunny, average day time temperatures 5C, but I expect this spot to be warmer than average.

I'm thinking things like miner's lettuce (which grows well here in winter in semi-sheltered spots), maybe silver beet.

I think the main issues are the pH, and how much root room there is (the one I weeded already seem full of root in places, but free in others).

Any ideas on what would grow well in that situation?

bump

Hi, Rosa, under olives in my region grow all sorts of wild allium spp, so I guess you could plant those, wild carrots grow well so you could plant carrots, mints (but they are a bit invasive some say), herbs grow well, I guess you could plant spinach ( I prefer planting spinach in late summer so it doesen't go to seed and I collect leafs all winter round), and in future think about climbers they love to grow on my olive trees. rosa canina grows well close to my olives, and even rubus spp grow well under olives maybe you could look into small shrubs that give berries, because some berries are really exuberant. it depends a lot on how big the olive trees are.
Don't worry for coffee grounds they won't have done any damage on the contrary, and if you put compost and wormcastings it will be great.

sorry, I didn't realise there had been replies to this.

It's spring now, I haven't planted anything yet, but am thinking about strawberries. I have plenty of plants in the garden I can transplant. I'm guessing the coffee grounds will help, but I don't want to do anything that will mess with the olives (they're not mine). If I add a couple of inches of worm compost and then mulch with something acidic (coffee or pine needles most likely) will this work for the strawbs without creating too much of a problem for the olives? Or will the acidity work its way down through all the soil? I gather olives can handle pH a bit either side, but they're in tubs so not sure if that makes them more sensitive.

Lorenzo, the trees are about person height. I don't want to plant anything that's too permanent as I'm renting. The pots the trees are in are probably root bound so I'm thinking things that aren't too deep rooted.