I have never come over any ATMs with dollars in Tanzania. I have lived in Arusha for a year (2004/2006) and have been there off and on since. I seriously doubt you will find any such ATMs. The country is however flooded with ATMs, though the one at Kilimanjaro airport was in disrepair around two months ago, last time I passed through that airport. ATMs with Tanzanian shillings (TSH) are available in most towns and along major roads.
You can usually get prices in Tanzanian shillings instead of dollars. Nobody are obliged to pay in dollars in Tanzania, although hotel owners and others may ask for dollars for many reasons.
It used to be like that, but I am sure not any more. Just checked with a friend of mine (tour operator) and they were quite sure.
The TANAPA (Tanzania National Parks) and many others also facilitate for payments using hand held VISA terminals.