My suggestion is not to buy this property. It will bleed cash. Its a bad deal. Find a better deal.
Paying $460K for $4300 in monthly rent is WAY too much to pay to generate any cash flow.
Paying 96% of market value is WAY too much to pay. You're almost in the hole with just purchase closing costs and certainly in the hole with sales closing costs if you have to sell.
This place costs $460K and you are qualified for $200K in financing and appear not to have the additional $260K on hand to close the deal.
You appear to be wanting to buy for one price using the bank loan and then have the seller carry a second without the bank's knowledge. That loan fraud. The only way you could use a seller second is if its fully disclosed to the lender and they approve it. Since they will include that debt in your DTI and qualification calculations, and they've already said you can only have $200K it seems unlikely they will approve a seller second for another $200 or whatever. Perhaps I misunderstand the situation.
Find a rental property that you can actually afford. One that's within the $200K loan amount plus whatever amount you have to put down.
Find one that actually cash flows. Use whatever terms the bank is offering (rate and term), calculate the P&I payment assuming 100% financed. Double it. That's the minimum rent you need to be break even. Better to do this in reverse, since rents are controlled by the market (that is, they're out of your control.) Take the market rent. Cut it in half. Use that as the payment, use the bank's rate and term, and calculate the present value. That's the most you can pay.
Find a property you can acquire at a significant discount to its market value. You lose 2-3% when you buy and another 8-11% when you sell. So you need at least a 10-14% discount off the market value just to be break even. Prices may continue to fall. You want some margin to handle any additional downward price changes.
If you can't do this stuff, don't buy rental properties! The goal here is to make money, not to own real estate. If you can't make money, don't buy it.