around that time=あの頃<ころ>anokoro/その頃<ころ>sonokoro
around this time=この頃<ころ>konokoro ※around these days=この頃<ごろ>konogoro
days
around September 23=くがつ にじゅう さんにちごろkugatsu nijuu sannichigoro
months
around September=くがつごろkugatsugoro
years
around 2050=にせん ごじゅうねんごろnisen gojuunengoro
※About Linda's answers
1. "jikoro" should be "jigoro"
2. We(Japanese) do not say "午前一時周り = Gozen ichiji mawari ". We say 午前一時頃<ごろ> = Gozen ichijigoro .