i made some testing and come up with the following solution which might give you the numbers you need:
Segment 1: New visits in the last 2 month
what it does: select all "visits" where visit number is "1" and time range is last 2 full month (must be added as "custom time range").

Attention: the numbers of "visits" and "unique visitors" are the same since you only select the "visit-container" with "visit => visit number = 1".
Segment 2: New visitors in the last 2 month
What it does: same as above, but show all visits of those visitors. it is same as above, but the visit condition is within a visitor container!

Segment 3: new visitors in the last 2 month with more than 1 visit
what it does: add segment 1 in a visitor container and "dublicate" for visits number greater 1. this way it selects visitors who had a visit with number 1 and a visit with a visit number greater than 1.

Segment 4: New visitors in the last 2 month with only 1 visit
What it does: same as Segment 2, but "exclude visitors with visits greater 1". you need to exclude a visitor container to really exclude all visitors who had more than one visit!

Calculated metric: Visits per visitor
what it does: show the average number of visits per visitor

==> FINAL TABLE
if you put all in one table, it would look like this (i hope you can read it ...)

i hope this helps 
kind regards
Urs