K.
Some babies are just like this. At first I thought it was something I was doing wrong because my son ALWAYS wanted to be held. Now that I have another child who doesn't mind being put down I know it's just a personality trait. The simplest solution is for you to wear your baby. Get a comfortable sling - I like kangaroo Korner adjustable fleece pouches for smaller babies, Storchenwiege or Didymos wrap slings for all babies and longer carries - and learn how to use it. www.thebabywearer.com can help. There are tons of great videos on you-tube of how to tie slings in different ways. You will have both hands free with a good sling. I can actually wear my 4-month old daughter and at the same time pick up my 2 1/2 year old son long enough to get him in and out of the swing at the park.
Other suggestions: he WILL get used to being set down, but you may need to find the right setting for him. My son fell in love with his Bumbo seat, so he was ok if I put him in that. Once he was a little bigger he was ok for short periods of time alone in the exersaucer too, and the jumperoo thingy too. Don't expect him to immediately be happy about it (or about being worn, if you've never worn him before). Give it 2 minutes the first day. 5 minutes the next, 10 minutes the next, etc. Babies are pretty adaptable, but you need to give them a chance to warm up to it.