when I was a newborn, back in 1973 my mom would carry me in a sling where ever she went as I was always gasping and highly emotional, especially after being diagnosed 4months late and under my birth-weight. Thank God my mom was a stay at home mom and had an abundant money source due to my grandma and father.
My Mom learned that putting me over her knee faced down while rocking her leg and knee at the same time back and forth helped, as it was a rocking motion, then she would pat me on the back to get the junk up while holding 1 arm at the same time. Play around with it, do more rocking then patting and perhaps do an occasional patting till your baby gets used to it... try not moving your knee but just your leg up and down. Perhaps you can try just holding her legs and see if she will be fine just hanging over your knee while being patted on the back, this could be a fun thing.
This method is simple enough and soothing, hope you find the method you are looking for.