About 20 Months
In general, events in the MCU happen around the same time as when the property is released. For example, Agents of SHIELD has a number of episodes that happen just before and just after the events of specific movies, and are released in tandem before and after the movie is. There are exceptions to this, but this seems to be the general rule. Avengers came out in 2012 so it happened in 2012. A year between releases in real life is generally a year between events in universe.
Since there isn't anything that implies seasons 1 and 2 of Luke Cage are back to back sequels, it probably follows this rule too. With the first season being released in the September of 2016 and the second being released in the June of 2018, we can assume there is somewhere between a year and a half and two years between the two seasons. There is some in universe evidence to help narrow this down.
Season 1 weather. At the start of season 1, the trees are full of green leaves. By the end of the season, the trees are bare and characters can be seen wearing warm hats. Judging off the weather we can guess that the season starts in early to mid September and ends in somewhere between late October and mid November.
Season 2 weather. The sun is shining and the sky is clear with green trees. It's summer!
Season 2: West Indian Carnival. The West Indian Carnival appears near the end of season 2, which happens each year in New York on Labour Day (first Monday in September). The season then probably spans from July to September.
Season 2: Misty's injury is fully healed. Following the events of The Defenders (August 2017), Misty Knight's injury has fully healed. We can assume this has taken at least a couple of months. From what we can see on screen she's not taking any painkillers (but is in rehab).
More evidence that a significant amount of time has passed (and not just a couple of months) includes: the Rand corporation building a new HQ, the lease on Pop's barbershop running out, Misty and Colleen's friendship building, the development of the "Harlem's Hero" app, etc. All things that take time.
So assuming season 1 ends in the November of 2016 and season 2 starts in the July of 2018, there is roughly 20 months between the two seasons.