Are there any Jewish writings that suggest the Earth rotates around the sun and is not the center of the universe?
Unfortunately, no - most Jewish sages until very recently insisted on the Sun rotating the Earth.
- The Talmud had some clear ideas of the sun circling outside a domed earth, moving through a window to the other side of the dome.
- Maimonides clearly describes the earth of being at a center around which the Moon, Sun, and the planets rotate.
- Rabbi Hayyim Vital writes about the earth being the center of "all of the worlds" like the pit of a date (עץ חיים שער א' ענף ד'):
נמצא כי כדור הארץ שאנו עומדים בו הנה הוא הנקודה האמצעית שבכל העולמות כולם כעין גרעין התמרה שהוא באמצע האוכל והאוכל מקיפו מכל צדדיו
- As recently as the 20th century, the last Chabad Rabbi insisted that the Earth actually rotates the Sun, and that this is compatible with modern science (which is technically partially true, but perhaps misleading)
Edit: The following article goes through a comprehensive list of sources from the 16th century onwards, showing that indeed no sources actually endorse the Copernican theory, with most rejecting it outright as blasphemy, up until the mid 19th century, with the Academic Rabbi Isaac Samuel Reggio supporting it.
*Though to prove this conclusively, we would need to go over every single source.
This answer is [only] a clarification of the previous answer:
There could be no authentic Jewish sources for claiming that the Earth rotates around the Sun other than ones that agree with the common science.
The reason is very simple - it has no practical Halachic implementations.
The only need to present the Solar system in its current form (Sun-centered) vs Earth-centered is to simplify the calculations of rotations of all other planets around the Sun. Technically, it is universally agreed that the physical Universe has no "center" and any point can be accepted as the center and the calculations made in accordance.
THe Jewish Halachah only uses 3 planets for all the practical laws: Earth, the Sun and the Moon. Even if we admit that the other planets (at least Venus, Mars and even Jupiter) were known in the ancient times, their rotation has no place in the Jewish Law and therefore the calculations are never mentioned.
NB: This dispute is similar to the dispute of calculating the orbits of space shuttles and satellites - whether Einstein's relativity must be used or Newton's laws work just fine. Turns out, most of the time Newton works just fine.
So a Sun-centered system presents no benefits whatsoever for calculating the Jewish times - daily, monthly or yearly.