I was earlier discussing how to calculate (or at least to constrain) satellite time in orbit. Such benchmarks matter where satellites need to mark time for position relative to L2 and the Umbra. (To L1, too.) Such also give the general optimum for ships in dock, where those ships hope to bounce ahead to L4 or behind to L5. That is: such matter for anyone needing to arrive or leave at the planet; if she's docking with a satellite in transit, before reaching the destination.
L2 is best as a momentum-bank attached to a swingin' tether. That means, cost-conscious passengers from/to Venus don't stay there.
Many outbound passengers are returnees who hope to board the same ships (or type thereof) they got here on, which should still be in orbit. Even for them, though, maintenance emergencies happen. People are going to need to wait out the time somewhere else, somewhere comfy. Let's look at satellites passing through a planetary umbra, with period synced up regularly with Hohmann Transfer windows for other destinations - with those timespans which allow the cheapest routes thereto. These satellites' orbits are eccentric, to direct ships taking that way out.
Start with Venus, Earth-facing. Note we are constrained - not by Hill a.k.a. "where L1/L2 at??", both which is a cool million; but by Sphere Of Influence. If my orbit takes me out of that, it is no longer an orbit but a trajectory, at best a solar orbit. Hop David's capture-radius numbers range 600000 km to 610238 km over surface = 616290 km with Wiki on the high-end 616000 km. But that's capture. Venus' orbiters need to stay under 536412 km.
As a maximum - for as long a "month" as I can get - I am making this circular as possible, so that orbit is semimajor. By Kepler here: 40.66 days on the true, sidereal track. The trajectory will, on a natural angle, pass through umbra once per its solar-synodic "orbit", 49.64447 days. That's 11.762 runs per the Venus/Earth synod so, let's bump that to 12:1 for 48.66 solar-synodic days. Its true, sidereal orbit at 1/(1/m+1/y): near exact forty Earth days. Semimajor 530567 km, 782 m/s - depending on when.
Hop David recommends five of these each on its own (slight) ellipse and angle. I'd consider a couple more. The flight to Earth is, I assume, Oberth.
Those who missed their flight to Earth can, on the next swing 'round, get to L4 in time to get aligned for the L4/Earth transfer. Although the outgoing liners do shake you down for the added fuel cost.
Of course anyone is welcome to stay here overnight for a trip up to L2 and its amenities. But L2 is exorbitant. The main transfer ship is zipping along at 29:1 where we left it (mostly) below us, rocking from 219335 to 536412 km. But only crew are staying there.
Below a certain level, I'd worry about flying the satellite through the walls of that magnetosheath cone. I do assume magnetic shielding against the sun on dayside, and against Venus' ions at nightside. Between the two, thrusters shouldn't be needed to maintain this period, just the magsail.
Ecliptic-retrograde serves emigrants off to L5, and stations with a need for more frequent passes through Umbra (though not spent in it). Some orbit more in line with the Venus-Mars synod. Most vital may be to send emergency supplies to incoming Hohmann; some of those should be in Venus-Earth.
RECALC 11/30, 12/9: tighten the constraint. ADD 3/13/21: Two more cyclers.
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