you can say 我想让你开心 = i want to make you happy

－ －＃ at first sight, i think is totally okay for saying so, but after having repeated it several times, turns out sort of inappropriate. when the subjective is a stuff/something, you can use ‘使’ for example: it / answering the phone call/ makes me happy/angry. 这件事／接电话 使我高兴／生气。 but when the subjective goes for a person, better use 让 instead. which is your case.

你可以说，我想让你高兴，听起来更自然。

I meant 怎样使别人开心呢 *