Since the input range of the MCP73213 goes all the way up to 16 V, I might choose a 12 V/1 A adapter instead. With respect to a 9 V/1 A adapter, that gives you another 3 W of headroom and it is a more ubiquitous value than 9 V.
Since this adapter is used for charging, it is not going to be run at 100% all the time. Once the cells get above a certain level of charge, the current will start to drop, so I don't see too much problems using a 1 A adapter, especially if it's a 12 V one.
In 24/7 applications, you really do want to go 20 or more % oversize. My ISP once gave me a modem with a 15 V/1 A adapter that was running close to its limits. Within a year and a half it died and they supplied me with a 1.5 A version. That one has been running ever since and must now have done some multiples of lifetime of the first one (yes, it is an old modem, but as long as they don't change any standards or I uprade my speed, they probably won't replace it). But it goes to show that some headroom may have a drastic increase on life expectancy.