You can say tomárselo con calma/ tranquilidad, although it generally refers to how you embark on a new project or face a task:
I have to write a paper, but since the deadline is in two weeks I'm taking it easy = Tengo que redactar un trabajo, pero como la fecha de entrega es en dos semanas me lo voy a tomar con tranquilidad.
[More examples here]
In the sense of "just chilling" tumbarse a la bartola (or also tirarse a la bartola) is indeed widely used (in Spain, at least) but it generally has negative connotations, as in being a loafer:
Estás todo el día tumbado/a a la bartola sin hacer nada. A ver si te buscas un trabajo ya.
(In case you're interested, the expression "tumbarse a la bartola" is said to find its origin in San Bartolomé day, on August 24, a day devoted to party and chill time when the season of the harvest was finally over.)
Some expressions with neutral or positive connotations are:
Relajarse (relaxing, chilling). You proposed relajando. Note, however, that the pronoun (me/te/se/nos/os) is mandatory here:
¿Qué haces?
Nada, relajándome un rato.
Pasar el rato (lit. letting time pass by, not doing anything in particular)
¿Qué haces?
Nada, pasando el rato.