I was wondering when this rifle was made serial # is 487786 it looks exactly like an 1890's but the barrel is round and not 6 sided.
Hello diverdown: A round barrel is possible/probable for your Model 1890 receiver, but only as a replacement barrel. Your receiver was serialized in 1912. Only late model 90 rifles - circa 1940 - are known to have original round barrels, and then not many. Your barrel is probably 23 inches long (as opposed to the 24-inch octagonal barrel - eight sided).
So the answer to your question is: original rifle 1912; replacement barrel: most likely in the very late 1930s to early-mid 40s.
If in good or better condition you still have a very nice Winchester that has a story to tell, but you only know part of it, and can dream the rest. The barrel was most likely made by Winchester (the inscription will tell you), and could have been replaced in the factory (if the barrel has a WP proof mark, or by a gunsmith (if the barrel has an OP proof.
The rifle should be .22 short, .22 long, or .22 WRF (not interchangeable).
Some collectors do not shy away from this combination, again if all Winchester parts.