It looks like authors choose "biān" or "bian" as the pinyin for 边 haphazardly at dict.cn:
东边 = dōng biān
上边 = shàng biān
右边 = yòu bian
左边 = zuǒ biān
旁边 = páng biān
外边 = wài bian
一边 = yī biān
两边 = liǎng biān
那边 = nà biān
这边 = zhè biān
里边 = lǐ biān
天边 = tiān biān
(There's also 海边, 身边, 内边, and 谁边.) It likewise seems haphazard at xiaoma.info.
Question: Can the pinyin for 边 be either "biān" or "bian" in general?
This question basically generalizes How come the first tone in the character of 边 in the word 东边 is not written?. Maybe there's cases where "biān" xor "bian" is the only strictly correct pinyin (or pronunciation).
dōng bian
in daily usage, but retroflexeddōng bianr
instead.