This is a very frightening and serious situation you're in here, as Psittacosis/Chlamydia is a very serious bacterial infection, and if not treated with the correct antibiotic at the EXACTLY CORRECT DOSAGE FOR YOUR BIRD'S WEIGHT, and for the correct daily frequency and length of days, is fatal...I know that you're in a situation where you have no Avian Vet near you...uhg.
First-off, no "syrups", as most "syrups" contain other ingredients that are harmful/fatal to birds, such as alcohol, tons of sugar, etc.
Oral Suspensions of antibiotics are usually the exact same formulation as the Injectable formulation, and that's what you want to give your bird orally. (You can't give a bird a tablet or capsule, obviously, and you certainly don't want to try to "compound" a tablet/capsule into an oral suspension/dose, because that's a process that you'll likely not get correct; too much antibiotic can make things worse, not enough antibiotic will be ineffective)...So you definitely wan oral suspensions that you will either have to give your bird directly into it's beak/mouth with an oral syringe, or by putting each entire dose in a bit of juice or in some type of food...HOWEVER, keep in-mind that if you put the dose of oral antibiotics into juice or food, your bird will have to eat or drink ALL OF THE food or juice to get the entire dose. So make sure that you don't mix the dose into a large amount of juice or food.
****You mentioned that he also is suffering from "Conjunctivitis" in one or both eyes, which is most-likely secondary to the Psittacosis. However, if it's not secondary to the Psittacosis and is being caused by a localized infection in one or both of his eyes, it may not be sensitive to the oral antibiotic that you're giving him for the Psittacosis; usually Conjuctivitis, whether it's being caused by a localized bacterial infection, a localized fungal infection, or it's photoconjunctivitis from him being under any type of artificial light/bird light/UVB light (I don't know if you've had him under any artificial lights, but if so, that's likely the cause), usually needs to be treated with a localized eye drop that is either an antibiotic or antifungal, depending on what microbe is causing it. If it's photoconjunctivitis due to him being under some type of artificial lighting, remove the lighting immediately and keep it off of him. Just keep in-mind that if his eye(s) don't clear-up with the oral antibiotic that you're giving him for the Psittacosis, then you've got another issue, a localized eye infection, that you're going to have to deal with separately. Watch it closely throughout the oral antibiotic treatment for the Psittacosis. It is probably secondary to the Psittacosis, but just watch it...Also, a sign that the Psittacosis is getting progressively worse and not clearing-up is the start of upper-respiratory symptoms, such as wheezing, coughing, open-mouth breathing, etc. So if he starts to display upper-respiratory symptoms, then you need to reconsider the treatment you're using.
Chlamydia psittaci, the bacteria that causes Psitticosis, is usually most-sensitive to Doxycycline, by-far...The other antibiotic that it is usually sensitive to is Tetracycline, but Doxycycline is the first drug of choice....I've not ever heard of treating Psittacosis with Azithromycin, and would not ever recommend using it, as Psittacosis chlamydia is not sensitive to it; OTHER STRAINS OF PSITTACOSIS BACTERIA ARE SENSITIVE TO AZITHROMYCIN, BUT NOT THIS ONE.
Has he already taken a round of Doxycycline? I couldn't tell if that's what you meant or not...If so, what was the dose, how many times a day, and for how many days?
If he hasn't yet taken anything, then you absolutely want to use an oral suspension of Doxycycline....Tetracycline is going to be your second choice of antibiotic; there are other antibiotics that are used as back-ups, one in particular, but should not be considered until you've already tried a proper dose and length of treatment with the Doxy and the Tetracycline.
Treatment needs to last 14 days!!! There is a very high-rate of relapse because the bird isn't given the antibiotic for a long enough time period, not because the Doxycycline wasn't effective...
I can help you with dosing, but again, I need to know what he has already been given, how much and for how long...And what does your bird weigh?
****I'll say this once again, THIS IS NOT THE WAY THIS SHOULD BE DONE, YOUR BIRD SHOULD BE TREATED BY A VET, AND I DON'T LIKE DOING THIS BECAUSE I AM NOT A VETERINARIAN. HOWEVER, I UNDERSTAND YOUR SITUATION AND WOULD RATHER HELP YOU GET YOUR BIRD ON THE CORRECT MEDICATION AT THE CORRECT DOSAGE FOR THE CORRECT LENGTH OF TIME THAN HAVE YOU JUST DO IT WILLY-NILLY AND HAVE YOUR BIRD SUFFER AND DIE...