I have exactly that problem with making doughnuts. It is difficult to prevent them from sticking to the basket. What I do is try to minimise the amount of liquid I put in them. This makes them easier to handle. I put them in the oil with two spoons. First I take a take a spoonful of doughnut batter and hold it just above the oil. I used the other spoon to push the batter off the first spoon.
For onion rings you could hang one on a fork(or hold with a tongs as somebody already suggested) with a spoon under to catch the drips.Then lower the spoon and fork into the hot oil. After a few seconds the batter will hopefully be cooked just enough to prevent it from sinking and sticking to the basket.