One of my favorites is Procatopus aberrans. There are two reasons for this. First, Aberrans is an attractive fish that grows to about 2 inches. Second, it has been an easy killie to keep and spawn, at least for me. I keep them in unsoftened Phoenix water that is very hard (I forget the measurements but remember it was 21 drops before the test vial changed color). They would probably do just fine if gradually introduced to softer water.
These fish are very active and require more space than a typical killifish. I have kept adults in 10-, 26-, and 55-gallon tanks. I actually prefer the 10-gallon size and set it up with a sponge filter, a spawning sponge, a little Java moss (or an artificial mop), a bare bottom, and a few Ramshorn snails. When my population outgrew the 10-gallon, they went into the 26-gallon and then the 55-gallon tank. With a small group comprising maybe 3 pairs, I would guess a 5- or 5 1/2-gallon tank would work, but I would not go any smaller. They need room to swim.
The adults are fed baby brine shrimp and flake food (primarily Brine Shrimp Direct Plankton and Spirlina flakes mixed with whatever else I have). I strongly recommend using a live food (baby brine shrimp, grindal worms, etc.) on a daily basis. Because I tend to overfeed, I keep Ramshorn snails in the 10-gallon tank. They remove the excess food. Ramshorns (even Pond Snails) work fine as long as you don't allow them to multiply into large numbers. The snails probably will consume a few newly-laid eggs, particularly if you use mops or plants as a spawning substrate, but the trade-off is better water quality.
When kept in the larger tanks, the Procatopus aberrans are frequently kept with other non-killie fish species. Because the Procatopus are relatively small and non-aggressive, you need to chose and monitor the mix. In the 55-gallon, I like the Julidochromis group as they primarily inhabit the lower levels while the Procatopus stay near the surface.
My fish room averages about 80 degrees Fahrenheit during half the year (summer) and about 70 the other half. With some fish, I notice a difference in spawning, but not for the Aberrans. Also, I have found that most of my killies appear to like the higher temps (as opposed to most killifish lore).
Breeding is simple. I use a clothes-pin to attach a piece of coarse filter foam / sponge to the inside of the tank. I found some discounted aquarium foam filter strips that measured about 10" x 3" x 3/4". The foam filter material was off-white or a very light yellow. It had large pores - bigger than a pin head/slightly smaller than a BB. I don't think a smaller pored material would work as well. One of these strips of filter foam is extended vertically into the water. The adults inject their eggs into the holes in the foam. One advantage to using foam is that larger snails cannot get into the pores (the fish inject their eggs fairly deeply).
It is always a good idea to offer a variety of spawning materials to your fish. Sometimes, they will surprise you. While I recommend the sponge material for Aberrans, I usually also keep a mop in the tank. Some species are not as attracted to the foam as the Aberrans and you will have better success with mops or live plants.
After a week or more (whenever I'm ready), I pull the strip of foam out of the adult tank and place it in a plastic shoebox. The water level in the shoeboxes is usually fairly high. Even then, it is seldom over 1 ½ inches deep. I throw in some larger Ramshorns and wait for the eggs to hatch.
As with most fish, the more water you have, the easier it is to keep from having something bad happen (the famous "margin of error"). With hard water, keeping snails in the shoeboxes lets you know when the water is going bad. The snails die first. That tells you it is time for a water change. As the eggs were laid over time, some fry hatch right away and some may take a week or more. The newly-hatched fry are fed baby brine shrimp (occasionally I have green water and am now keeping vinegar eels which should work nicely too). Later, they are fed baby brine shrimp only until they graduate into larger quarters. The shoebox may or may not have some Java Moss. There is no filter, but if the shoebox is located near a source of air, I may place an air-stem at one end, and let it bubble gently.
How long I keep fish in shoe boxes depends upon many factors, but the primary one is probably space availability. You can grow fry to adult size in a shoebox, depending upon the number of fish. If there is a large hatch, as they grow, they get moved to sweater or blanket boxes as needed. If there is a small hatch and there isn't anything larger available, they stay in the shoebox. I have kept Aberrans, about one-inch long, in the same shoebox since hatching - no filter, no air stem, and just fed baby brine shrimp.
As an aside, you will find fry swimming in the parent's tank from time to time, but they disappear shortly. I have not observed it, but believe the adults will predate the fry. That is why you move the foam spawning material to a shoebox.
So, if you are looking for a Lampeye, a different kind of killifish, try Procatopus aberrans...