Having spent quite some time in especially Eastern Africa and in total also a month in southern Africa, I have seen about 40 species of antelope during that time.
As you have only a month, I would advise you to stick to only 1 or 2 countries. Travelling in Africa takes time and the faster (less slow) modes of transport (own 4x4 / plane) are expensive. In addition to that lodging is often expensive and entrance fees for the national parks as well....
Depending on how much you have travelled and how much hassle you can stand, I would advise you either going to South Africa ( with a possible extension to Botswana) or Kenya (you could add Uganda to this, northern Tanzania does not have different species then most of Kenya). South Africa is much easier to travel around and more hassle free.
For South Africa, I would start in Cape Town and making your way to Kruger from there. Along the route you could pick up many Cape and Karoo & Highveldt specials like Cape grysbok, Grey rhebok, bontebok, black wildebeest etc. Where Kruger has many of the more standard savannah species, but also nyala which is rather restricted in it's range. If time allows it would be worth to travel to northern Botswana and visit Moremi and/or Chobe, these places hold Tsessebe, red lechwe and Chobe even has some puku.
Hirola can be seen in Tsavo east in Kenya, which is a safe area, though these are an introduced group... The Tsavo ecosystem also holds some east African specialities like lesser kudu, gerenuk & Beisa/Galla/Fringe-eared oryx and multiple dikdik species. Combine this with the species of the southern Kenyan savanna like Coke's hartebeest, wildebeest, steenbok, grant's & thomson gazelle. Mountain bongo are found on Mt. Kenya and in the Aberdares range, though they are tricky to find apparently. If you would be able to add Uganda, you add the possibility of Ugandan kob and several duiker species (weyns, yellow-backed, rwenzori).
A good starting point would have been the book "the Antelope of Africa", but this is currently being reprinted and unavailable... The Kingdon field guide to African mammals is another good starting point as is "the bovids of the world", but due to oversplitting it is easy to get lost in this book...