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I am aware that Daniel lived during the time of Purim (as there are opinions he was Memuchan). This led me to think: is there a rough timeline with the 24 books of Tanach and their corresponding years? Either Hebrew or English year.
I am curious to see which of the books of Neviim and Ketuvim were written closely together. Clearly, the story of Daniel and Megillas Esther had to be written within a similar time frame.
Seder Olam Rabbah provides the basis of the traditional Jewish chronology of the Tanach. Corresponding years can be seen in the timeline that @sabbahillel linked. With regards to your wanting to see who lived more or less when and when the different events in the various books happened, I have attempted to organize everything.
Note: Since Divrei Hayamim (DH) encompasses practically all of Tanach, the various verses will be interspersed throughout the timeline. Calculations of the times of the genealogical verses of DH are based mostly on a chart I made not long ago.
The beginning of the Torah - most of Beresheet - is of course the oldest. DH 1:1 covers everything from Adam to the kings of Edom (Beresheet 36:31-43). Then there's a disagreement about when exactly Iyov took place: He could have been anywhere from the time of the Avot to after the end of the Babylonian exile. After that, there's the rest of the Torah. DH 1:2:1-5, DH 1:2:18-21, DH 1:2:24-28, DH 1:2:31, DH 1:2:42-49, DH 1:4:21-26, DH 1:5:1-3, DH 1:5:27-30, DH 1:7:6-12, DH 1:7:1-2, DH 1:7:20-27, DH 1:7:30-37, DH 1:8:1-7. Some parts of Tehillim are attributed to Moshe. DH 1:2:7-81, DH 1:4:1, DH 1:4:4-10, DH 1:4:13, DH 1:4:15, DH 1:5:31, DH 1:6:1-9, DH 1:6:14-15, DH 1:6:35, DH 1:2:22-23, DH 1:8-11, DH 1:23:13-24, DH 1:24:19-30, DH 1:27:21-27 circa the last 20-30 in the desert, along with the first conquests east of the Jordan.
Then there's Yehoshua. DH 1:2:12, DH 1:2:27-33, DH 1:2:50-55, DH 1:4:2-3, DH 1:4:11-12, DH 1:4:14, DH 1:4:26-31, DH 1:5:30-31, DH 1:6:6, DH 1:6:9, DH 1:6:14-15, DH 1:6:36-37, DH 1:6:39-66, DH 1:7:28-29, DH 1:7:39-40, DH 1:8:12-29.
Shoftim opens up after the death of Yehoshua, but the second conquest story, that of Kiryat Sefer, describes a story that, according to the version in Yehoshua, took place before the death of Yehoshua. Pilegesh in the Givah most likely took place not long after the death of Yehoshua, given that the elders are the leaders and Pinchas was still active as Kohen Gadol. Likely Pesel Micha and the northern conquest of Dan were also around that time2. DH 1:2:11 from circa Yehoshua's death until circa Ivtzan. According to the opening of Ruth, that story also took place during the time of the Shoftim. Rashi per the gemara says it happened circa the rule of Ivtzan, as Ivtzan was Boaz. DH 1:2:34-37 from circa Gidon until circa Shmuel. DH 1:4:3 from circa Avimelech until circa Shimshon3. DH 1:5:31-33 from circa the death of Yehoshua to circa Shmuel. DH 1:6:10-12 from circa Yiftach to circa Eli. DH 1:8:29-33, DH 1:9:35-39 from circa Eli to circa Shmuel.
Shmuel is next, with Eli and Shmuel being the last judges before the change to governance by king. Eli was already quite old by the time Shmuel starts. DH 1:6:13, DH 1:8:33. Shaul is crowned. DH 1:2:13-17, DH 1:2:38, DH 1:5:9-10, DH 1:5:34, DH 1:8:34, DH 1:9:39-40. David is crowned. DH 1:12, DH 1:10, DH 1:3:1-4, DH 1:11:1-9, DH 1:3:5-10, DH 1:6:16-33, DH 1:9:21-22, DH 1:11:10-47, DH 1:13-29. Large portions of Tehillim were written during the reign of David by David and the Levite leaders of the time - Asaph, Heiman and Yedutun.
Then Melachim. Sometime during the reign of Shlomo, he wrote Kohelet, Shir Hashirim and Mishlei. DH 2:1-9, DH 1:5:34. Rechavam. DH 2:10-13, DH 1:5:35, DH 1:8:35, DH 1:9:41. Aviyah. DH 2:14, DH 1:5:35, DH 1:8:36, DH 1:9:42. Asa. DH 2:15-16, DH 1:5:35, DH 1:8:36, DH 1:9:42. Yehoshafat. DH 2:17-20, DH 1:5:36, DH 1:8:36, DH 1:9:42. Yehoram. DH 2:21, DH 1:5:37, DH 1:8:36, DH 1:9:43. Achazyahu. DH 2:22:1-10, DH 1:5:37, DH 1:8:37, DH 1:9:43. Atalyahu. DH 2:22:11-23. Yoash. DH 2:23-24. DH 1:5:38, DH 1:8:37, DH 1:9:43. Amatzyah. DH 2:25, DH 1:5:38, DH 1:8:38, DH 1:9:43. Uzziyahu. DH 2:26, DH 1:5:38, DH 1:8:38, DH 1:9:43. Yotam. DH 2:27, DH 1:5:39, DH 1:8:38, DH 1:9:43, DH 1:5:11-17, DH 1:5:18-224. Achaz. DH 2:28, DH 1:5:39, DH 1:8:39, DH 1:9:43, DH 1:5:4-9. Chizkiyahu. DH 2:29-32, DH 1:8:39-40, DH 1:4:34-43, Mishlei 25:1. Menashe. DH 2:33:1-20, DH 1:8:40, DH 1:9:44. Amon. DH 2:33:21-25. Yoshiyahu. DH 2:34:1-35:1-25, DH 1:5:39. Yehoachaz. DH 2:35:26-27, DH 2:36:1-4, DH 1:5:40. Yehoyakim. DH 2:36:5-8. Yehoyachin. DH 2:36:9-10. Tzidkiyahu. DH 2:36:11-21, DH 1:5:40-41.
Most of Trei Asar are spread out across the timeline of Melachim5. Ovadiyah is thought by some to have been the Ovadiyahu who was an important servant in the government of Achav (see Melachim 1:18). Yonah was probably next, a prophet during the time of King Yerov'am II, but quite possibly a student of Elisha before that (see here). Yoel may have been around the time of Yonah, because there's one phrase that appears only in their books: דם נקיא (with that spelling). Hoshea was active during the reign of Uzziyahu, Yotam, Achaz and Chizkiyahu, as was Yesha'ayhu, although it is believed by some that Yesha'ayahu was Hoshea's student, being that he seems to quote him sometimes. Amos was also active during the time of Uzziyahu and Yerovam II. Amos also appears to be quoting Hoshea, so may have also been a student of his. Micha was active during the reign of Yotam, Achaz and Chizkiyahu, quotes Yesha'ayahu, and some even think he was also active during the time of Menashe (see here). Nachum also quotes Yesha'ayahu. Chavakuk quotes Micha. Tzephanyah was active during the time of Yoshiyahu and also quotes Yesha'ayahu. Yirmiyahu was active during the time of Yoshiyahu, Yehoazchaz, Yehoyakim, Yehoyachin and Tzidkiyahu. Around this time he wrote Eicha as well (see here). During the exile of Yehoyachin but before the destruction of the Temple, Yechezkel prophesied in Babylon. Daniel became prominent from the time of the exile of Yehoyachin and was active until the time of Daryavesh ben Esther (see here). Some chapters of Tehillim can be attributed to this time, notably Tehillim 137.
Ezra starts in the beginning of the reign of Koresh who ruled after Daryavesh the Mede, who defeated the Babylonians. Tehillim 126, DH 2:36:22-23, Ezra 1:1-4:1-5. Ezra 4:6-24 was during the time of Achashverosh/Artachshasta (I), as was Esther. Daryavesh ben Esther assumed the throne. Ezra 5:1-2. Chaggai and Zecharyah prophesied around this time. Ezra 5:3-Nechemiah 13 also took place during the reign of Daryavesh ben Esther, aka Artachshasta (II). Per Malbim, DH 1:9:1-34 is parallel to Nechemiah 11. Malachi prophesied somewhere around this time. DH 1:3:19-24 spans this era.
1 Achar is Achan who plays an important (negative) role in the conquest of the Ai story in Yehoshua.
2 Per Yechezkel Kaufmann, among others.
3 According to the gemara and the midrash, Hatzlalpuni was Shimshon's mother (see also here).
4 Per Da'at Mikra.
5 Calculations of Trei Asar per Rabbi Ahron Marcus in his book Barzilai.
The latest Koren Tanach has a graphical timeline of the 24 books which I hope answers your question.
The timeline of the world from the creation of the world through the destruction of the second temple in 68 CE can be derived from the references in TANACH (as shown in Seder Olam). As an example, the list of births in Genesis show when each generation was born. A timeline display in the Art Scroll Noach shows the dates from Creation through the death of Yaakov in 2255. The remainder of the Chumash covers from the birth of Moshe in 2328 through the arrival of the Jews in Israel in 2488. The first temple was built by Solomon in 2928 and destroyed in 3338. Purim was in 3400. The second Temple was built in 3408 which ended the period of Tanach. The second temple was destroyed in 3828.
A typical timeline is shown from Creation through the assassination of Yitzchak Rabin in 5756 (1995).
