I'd like to help a $6$ year old who already has a pretty good grasp of $2$, $5$, and $10$ times tables.
I'm guessing you are looking for a hard data research answer, but unfortunately, the studies I know of are dubious, partly because they rely heavily on learning style myths, partly because some are funded by commercial parties pushing particular systems.
However, I can give some general advice --
Give the system for the 9s that the digits add to 9, let your pupil fiddle with the patterns, and they tend to get this one fairly quickly.
Asian countries do fairly well with a "musical" or "chant" method. I've heard of a couple commercial products, including Times Table Rap.
Play with the visual representation using marbles or tokens, especially so the pupil can understand why 3 x 7 is the same as 7 x 3.
The "circle" method of visualizing skip counting (samples of what I mean here) can be brought in to help with understanding the "rotating" nature of counting on the times tables.
There are a fair number of games that help multiplication table prowess, either intentionally or unintentionally. Yahtzee in particular naturally covers the 1-6 portion of the table. I've written a game myself, although I don't know how well it would work with 6 year olds.
While I wouldn't necessarily recommend the DS game itself, check out how Professor Kageyama's Maths Training: The Hundred Cell Calculation Method mixes up the columns and rows of the times table to force students to think about the arrangement.
My personal experience with my 7/8 year old is that Math War works very well for practice. You can play with a normal deck of cards---each player plays two cards, and announces the product, with the higher number winning all the cards. In case of tie, then there is "War", which means you put two (or more) cards face down and then have aother battle on top, with the winner taking the whole pile. You can also play the game with any set of ordinary flash cards. My son is interested to go for a long time with this...
I would also add, however, that although I have heard many people say that one must master the basic math facts before learning more advanced math concepts, I think that this is nonsense. Go ahead and talk about any kind of mathematics (at the right level) with your child.