Here in Michigan the coyotes mate mid February thru March, a few may be later.
With a lactation period of 60 to 70 days you should start seeing pups late April to the end of May at den sites. We do not normally start seeing pups hunting with mom or dad till late June into July.
Pups start dispersing from their natal territories as early as 6-9 months of age, or they may remain as subordinate associates.
We have had a closed season on coyotes at the end of March till Oct for years so never kept track of pups all that much till last summer when our season is went to 12 months of the year.
Last summer I didn't do much coyote hunting due to knee replacement surgery and my friends placing me in easy access spots.
I don't worry much about shooting a lactating female because dad & older siblings make good baby sitter and keeps them fed with game they eat and regurgitates for them.

Al