Didst on the sly is an old-fashioned way of saying "did secretly" or "did covertly". If you're looking for synonyms to replace this archaic phrase, there are plenty of modern alternatives. Words like "covertly", "surreptitiously", and "furtively" all convey the same meaning as didst on the sly and are commonly used in contemporary English. You could also use more informal language such as "snuck around", "behind someone's back", or "on the down-low". The important thing is to choose a word or phrase that fits your style and conveys the meaning you want. So don't be afraid to experiment and find the right synonym for didst on the sly.