While we can't date the more popular publications, Philodemus provides an unusually-well-documented list of Epistles, dated per each Archon. Clay preserves this list (51-54):
(forgive the formatting errors)
YEAR/S - Archon Name
- Epistle No. Common name (reference).
307/6 - Anaxikrates
The date of Epicurus' move to Athens, Diogenes Laertius, X.2.)
300/299 - Hegemachos
- No. 1. Peri phuseos Book XV (Arrighetti, p. 292).
296/5 - Nikias
- No. 2. Peri phuseos Book XXVIII (Arrighetti, p. 321).
- No. 3. A letter written eri Nikíov, Philodemos, On Epicurus II, fr. 1.7 (Vogliano, p. 59).
294/3 - Olympiodoros
- No. 4. A letter to a person unknown, from Philodemos, Праумаа XIV.11
292/1 - Philippos
- No. 5. A letter to Polyainos and Leonteus of Lampsakos on the Stoics in Athens, Pap.Herc. 176, fr. 5, XXIV. 14-15 (Vogliano, p. 50; Arrighetti, [67]).
- No. 6. To Themista of Lampsakos reporting on the young Pythokles, Philodemos, Пра MOTEiaL IV.8-10 (Arrighetti, [501).
- No. 7. To friends in Lampsakos on poverty, Philodemos, On Wealth XXXV.38 (Tepedino Guerra, p. 67; Arrighetti, [96]).
291/0 - Charinos
- No. 8. Letters sent to Polyainos, Charino magistratu, Seneca, Epistulae 18.9 (Arrighetti, [831).
- No. 9. A letter to Polyainos, Philodemos, On Epicurus, fr. 5.1 (Vogliano, p. 65; Arrighetti [841).
- No. 10. A letter to a person unknown, Philodemos, On Piety, Pap. Herc. 1098, X. 12 (Gomperz, p. 125; Arrighetti, [106] [lines 938-939 Obbink]).
- No. 11. To a person unknown, Philodemos, On Piety, Pap. Herc. 1077, X.1 (Gomperz, p. 105; Arrighetti, [107] [lines 840-841 Obbink]).
- No. 12. To Polyainos on poverty, Philodemos, On Wealth XXXIV.8 (Tepedino Guerra, p. 66; Arrighetti. (1081).
- No. 13. A letter to a person unknown, Philodemos, On Wealth XXXV.8 (Tepedino Guerra, p. 67; Arrighetti, [109]).
290/289 - Telokles
- No. 14. To Mithres, on a reversal of fortune, Philodemos, On Wealth XXXVI.9 (Tepedino Guerra, p. 67; Arrighetti, [791).
289/8 - Aristonymos
- No. 15. To Mithres, acknowledging a contribution to the school, Philodemos, Прааеа XXXIV.1 (Diano, p. 32; Arrighetti, [74]).
- No. 16. To Phyrson of Kolophon on the piety of a certain Theodotos. Philodemos. On Piety, Pap. Herc. 1098, XII. 15 (Gomperz, p. 127; Arrighetti, [93] [lines 797-801 Obbink]).
286/5 Diokles
- No. 17. A letter to Anaxarchos and Leontion, Pap. Herc. 176, fr. 5, XXV.31-32 (Vogliano, p. 51).
285/4 Diotimos
- No. 18. To Phyrson, Philodemos, Прауата XV.1-2 (Arrighetti, [94]).
- No. 19. If the name Diotimos is that of the archon; cf. No. 11. A Diotimos appears in Pap. Herc. 1780, VIII, fr. 1 [On Piety, lines 841-842 Obbink]. If he is Diotimos Euvóotov EnuaxiSns he cannot be the recipient of a letter from Epicurus; cf. W. Croenert, Kolotes und Menedemos, Leipzig 1906, pp. 82-83.
284/3 Isaios
- No. 20. To a person unknown, Philodemos, Прауратє XXXII. 14 (Diano, p. 19; Arrighetti, [110]).
- No. 21. To a person unknown, apparently on the education of the sons of Menoikeus, Phi- lodemos, adv. [Sophistas], fr. 16 (Sbordone 1947, p. 78; Arrighetti, [111]).
283/2 Euthios
- No. 22. On a setback of the Macedonians to a person unknown, Philodemos, On the Stoics, Pap. Herc. 339, V.9 (Arrighetti, [112]) [**Gli Stoici" VI.9 Dorandi].
281/0 Ourios
- No. 23. To Leonteus, Philodemos, Iayatr XXXII.15-16 (Diano, p. 19; Arrighetti, [68]).
279/8 Anaxikrates
- No. 24. To a person unknown, Philodemos, On the Stoics V.13, En'] 'Avatuk[p]á[rous (cf. Croenert [under No. 19], p. 54, n. 259) [*Gli Stoici" VI.13 Dorandil.
278/7 Demokles
- No. 25. To Kolotes of Lampsakos, possibly on the death of Metrodoros, Pap. Herc. 176, fr. 5, XXVIII.3-4 (Vogliano, p. 54 [cf. Gomperz in Hermes 5, 1871, pp. 387-388]; Arrighetti,[62]).
- No. 26. To Mithres, Philodemos, Maya XXIX. 17 (Diano, p. 15; Arrighetti, [75]).
274/3 Euboulos
- No. 27. To Idomeneus of Lampsakos, Philodemos, Прауцат XXVI.14 (Diano, p.12; Arrighetti, [601).
- No. 28. To Mithres on frugality, Philodemos.Прауатїа XXX.16-17 (Diano, p. 16; Arrighetti, [76]).
- No. 29. To a person unknown, asking for somebooks of Demokritos, Philodemos, adv. [Sophistas], fr. 13 (Sbordone 1947, p. 75; Arrighetti, [113]).
271/0 Pytharatos
- No. 30. To Mithres on his approaching death, Philodemos, Прауатеа XXXI.3-4 (Diano, p. 17; Arrighetti, [77])
I note that Epicurus maintained a correspondence with Mithres for over two decades.