You would say "I've been studying Japanese lately." in Japanese, too. I'm a native Japanese speaker, and I would say so personally.
"Saikin Nihongo o(wo) benkyou *shite imasu."
(*"shite imasu" is more formal than "shite masu." In conversation, "shite masu" is more often heard.)
If you say, "ima wa", then the particle "wa" emphasizes the temporariness of the action. (You've been doing it for now, but you may stop at any time.)
You could say, "ima nihongo o(wo) benkyou shite imasu" to say your current situation.