What are you giving? Sounds like it's penicillin, since it sounds like they're getting shots for several days? If it's penicillin, I don't think there is a way--in my experience, all horses get tired of penicillin injections, and I know I sure hate giving them. That is why if it is at all possible to avoid, I DON'T give penicillin! For respiratory infections if I give anything at all it is an oral drug--Uniprim. If I must give something stronger then I use Excenel--4 or 5 days of shots, but it's a relatively small dose compared to penicillin. If I have to give penicillin then if the vet says it works okay I use the long acting variety, so that they don't get shots every day, just every 2nd day--anything that helps!! I haven't had to give the dreaded daily penicillin shots in many, many years now!
Most of my youngsters don't take exception to the ordinary vaccines. One filly the one year did really get offended by her first spring shot--she was a total pet and after she had her first shot she started acting like I was a horrible monster that was out to kill her, and she wouldn't let me near her! Even bribing her with oats didn't help--she'd take the oats but then the next time she saw me she acted like she was terrified of me again. Then I went out with the cordless clippers & started clipping her buddy. When she saw what I was doing Misty knew that was harmless--Misty likes to be clipped, so she came over & pushed in for her turn! From there she was okay again, and when the time came to give her the 2nd doses of vaccines she took it much better than the first time around.
In any case, if you're having to give daily shots right now you're likely going to have to just catch the little ones any way you can & give them their medication, and once you're finished go back to regaining their trust.