Judaism in modern America has always been heavily influenced by the practices of our Christian neighbors, if only because of proximity. The convention of sermonizing was mostly foreign to the faith until the Reform movement adopted it in the late 19th century, though many 21st century congregations prefer the more study-base D'var Torah at their Shabbat services. Some older synagogues have pews instead of chairs, a brief and rather poorly received change first instituted by Reform movement pioneer Isaac Mayer Wise. Of all the Christian-influenced conventions in Judaism, one of the most pervasive and enduring is the Sunday religion school. Sunday has no particular importance in Jewish ritual and it should be noted that classical Jewish communities didn't limit religious education at the local synagogue to just one day a week. Sunday school is a natural outgrowth of the demands of secular American culture. Simply, children go to secular school Monday through Friday, it's impractical to ask people to devote their evenings to yet more study and Saturday has been more or less claimed as the culture-wide day of leisure. So, Sunday belongs to religious education, regardless of one's affiliation.
The problem with Jewish religion school in the Sunday format isn't so much the day on which it takes place, but the way the standard arrangement doesn't really mesh with the rest of the community. Jewish religion school is an ever-shifting thing. The way it looked in most Reform congregations in the early 1990's is drastically different than its current incarnation. What began as formless, multi-subject classes transitioned in many synagogues to a rotating system of specialized classes. In other words, a classic elementary school model vs. a standard high school model.
But this doesn't really get at the core of the problem. Judaism is incredibly dependent on community involvement. Separating students by age and subject matter runs counter to the way the rest of daily religious life works. It would be more fitting to create a flexible, mixed-age system that requires older students to actively participate in the education of younger students. Just like in the Torah portion Parasha Yitro, the government-establishing conversation between Moses and his father-in-law Jethro, the community can become more efficient and interconnected by simple delegation.
After all, Jewish lessons are inherently layered. Every story in the Torah, every philosophical discussion in the Talmud and every holiday ritual has multiple levels of meaning. The parable-style surface of a lesson is an entry point for young children, the deeper symbolic layers for those coming of age and the grand, uniting morals for those ascending to adult responsibility. It's vital that Jewish youths are asked to actively participate in the growth and maintenance of their community, rather than being cordoned off in classrooms.
It's also important to give their parents a reason to stick around. Still today many synagogues have no Sunday programming for parents who drop their kids off for religion school. Something as simple as an informal brunch with some learning opportunities and, as above, a chance to participate in the education of the children would do wonders for building a community in action instead of just in name.