The phrase 'would occasionally make' is correct and usable in written English.
You should use it when you are talking about an action that was done periodically, usually with some degree of irregularity. For example, "The couple would occasionally make trips to the nearby lake for a weekend getaway."
His incessant questions grew tedious and I would occasionally make up a silly answer.
Johnson, wearing a white doctor's coat, would occasionally make a discreet entrance to take measurements of erogenous zones.
When he was the defensive coordinator for the Giants, Broncos Coach John Fox would occasionally make the short trip from Rutherford, N.J., to Mt. Laurel.
Although a fan of the press, Moses acknowledged Ipso would occasionally make unpopular decisions: "But we are not here to be popular.
The military regime in Burma (now Myanmar) would occasionally make trouble on the border, but was no more than an irritant to the generals, who would usually be worsted.
There, the cooks — Sophia Wang Ms. Liuu's sister-in-law), Mei Lee and Mg Naing — would occasionally make off-menu dishes from their native Myanmar, for those who knew to ask for them.
The usual whispers of off-the-set problems and failed tabloid romances would also occasionally make the rounds.
Guys I would occasionally have sex with, maybe only make out with, but never be allowed to say they were my boyfriend.' That, he suggests, was perfect for songwriting, because he would always be longing for something.
…and would occasionally produce results like this….
For environmental reasons, the new boardwalk and all future boardwalks within the city will be made of concrete and plastic, although Smith allowed that exceptions would occasionally be made for spot repairs.
Imagine how lacking in sparkle our everyday existences would be if we didn't occasionally make absurd decisions, such as jumping in a fountain fully-clothed, belching loudly at a Christening or marrying our cousin.
