Warlock 5, Cleric 5
When considering options for consistently resurrecting creatures, Revify (3rd level spell) is clearly the way to go, since otherwise we'd need access to 5th level slots. This does pose a problem however, since Revify only works within a minute of death, and the Chronicle of the Raven Queen invocation also requires a minute to work. So we'll need to employ Gentle Repose (2nd level spell) as well to extend the amount of time we have to use Revify, along with enough slots to run each of these five times per Long Rest.
With that plan in action, we need to get the Warlock to level 5 to gain access to two 3rd level spell slots per Short Rest, and Cleric to level 5 as well to gain access to both the previously mentioned spells, as well as to feed the additional spell slots needed. Life Domain Cleric has the bonus of granting Revify at 5th level, though this isn't mandatory.
Our relevant spell slots are now:
- Warlock: 2 x 3rd
- Cleric: 3 x 2nd, 2 x 3rd
The last thing we need to consider for pulling this off is cost. Revify is the cheapest of the resurrection spells that can be done more than once per Long Rest, but it still requires 300 gp worth of diamonds per casting. Based on your source of average amount of money from hoards by level, one hoard altogether at level 10 would grant 20100 gp worth, which is enough for 67 castings per hoard. Adding the median amount of individual monster treasure at level 10 would increase that to 71 castings. More realistically this money would be split between a party, but as long as you're fairly active at hunting down hoards you could potentially keep the flow of money coming enough to sustain this lifestyle choice.
Following a long rest, we can initially kill, Gentle Repose, Chronicle, and Revify the creature a total of three times, with one 3rd level spell remaining from the Cleric. We then take a Short Rest to regain two more 3rd level Warlock slots, which we expend to Gentle Repose and Revify, completing a fourth cycle. A second Short Rest lets us do this once more for a total of five.
But there is another optimization we can make. If our Warlock were to come upon a Rod of the Pact Keeper, they would be allowed to regain a Warlock spell slot once per Long Rest. Using this before the first Short Rest would allow us to pair it with our leftover 3rd level Cleric slot to bring that up to four times. With this setup, only one Short Rest would be needed to complete the final cycle.
Five levels of Warlock and five levels of Cleric, combined with the Rod of the Pact Keeper, would allow us to use Gentle Repose and Revify to resurrect a creature five times per Long Rest, with a single Short Rest in between. Component cost: 300 gp per cycle, 1500 gp for all five.
After a single Long Rest with this setup, and Short Rests after each casting after (minus one hour's worth to account for the actual casting and Chronicle times), the character could pull off 27 resurrections per day.
Addendum: Divine Soul Sorcerer
As Jamie Katz points out in their answer, you can take advantage of the Divine Soul Sorcerer to gain the Cleric spells you need, while also exploiting the Sorcerer's spell point system to accomplish this as low as level 8, given sufficient Short Rests to convert the slots. This isn't to reiterate their excellent improvement, but rather to consider the benefits of applying the same trick here with a level 10 Warlock/Sorcerer instead.
Taking this route, you could convert your 5 sorcery points into a level 3 slot, and three level 1 spell slots into two level 2 slots, which gives you five level 2 and five level 3 slots total: enough to pull it off without a Short Rest or the Rod of the Pact Keeper, and with a level 1 slot left over.
Combined with proper spell point conversions on a Short Rest each hour, you could then pull off 34 of these resurrections per day on a single Long Rest.