I suppose that it might be possible to blanket-train a baby without using physical pain, but the alternatives I could think of are not too great, either. Blanket training is exactly the same principle as teaching a dog to "stay", and is meant to be even more simplistic, because usually dogs are at the adolescent stage when they get that concept, so their brains are more mature in relative terms. You might be able to do it with rewards rather than aversion, but what would that be? Candy? An actual hug? With dogs, a training reward has to be something that is never made available under any other circumstance, and it has to be something REALLY compelling, which is a really tough choice when it comes to human infants, because there is almost nothing that they want that badly that they won't drop it instantly in favor of the next new thing, at least for a while. To be honest, the only thing I can think of that might consistently work as that kind of positive reinforcement for a child that young is maternal touch, but you would have to withhold it at other times in order to make it effective in this context. We know that all of the Duggar children were weaned at 9 mos, so obviously she held them often until then. I think that striking the child is really the most likely effective scenario.
Note: I reread the book passage in which Michelle described her blanket training method, and the mention of a toy is a bit confusing in context of the usual method that the Pearls taught. What she meant about the toy was that she allows the child to have one quiet toy while on the blanket, and the toy is not taken away or used as an off-blanket object of desire. The toy is the consolation object, if you will, the one thing they are allowed to control while there (though she does say that if the toy is thrown off the blanket it will not be retrieved that session.) However, the child can only play with the toy quietly and in a seated position. They are also not allowed to stand or crawl within the border of the blanket -- that also earns "correction" (which is described as mother's voice, but different than usual and unpleasant.) "Encouragement" is used only when or if the child fails to respond to verbal "correction".