Well the best option would obviously be to not overload the liver at all, though that isn't necessarily available. Curcumin is very good for the liver. It up-regulates a number of phase I and II detoxification pathways, meaning that things can move through more quickly. It also stimulates gall-bladder emptying, which literally dumps the contents of your liver out into the small intestine. You could then also use something to bind to the toxins in the gut such as chlorella, which conveniently has some broad-spectrum antimicrobial activity so may theoretically be beneficial in SIBO. If you choose to use chlorella you need to be careful to start at a low dose otherwise you could give yourself a rough ride.
If you are really overloading your liver then silymarin (milk thistle) is also good, but I wouldn't recommend it as a first line of defence as it actually protects the liver by slowing down a number of liver processes, thereby preventing the uptake of toxins into hepatocytes. This is good for the liver, but not necessarily great for eliminating toxins from the body.
Here is a very detailed paper on how food influence the different detoxification pathways in the liver. It is a pretty detailed paper so you would really need to sit down and focus on it to get anything out of it. You will notice that whilst a certain food may have a particular influence on the liver at one dose, it can have the complete opposite impact at another dose.
https://www.hindawi.com/journals/jn...tm_source=plus.google.com&utm_campaign=buffer
I wouldn't get too hung up eating only things that improve liver function, but it is worthwhile knowing what will aid detoxification and what will hinder it. It is also good to know what the different types of liver detoxification are.
You could also try supplementing with something like acetyl-glutathione, or taking glutathione precursors like undenatured whey or ALA. Start low if trying glutathione and its precursors.